Investigation of the Effect of a Circular Patch of Vegetation on Turbulence
Generation and Sediment Deposition Using Four Case Studies
By
Alejandra C.Ortiz
B.A., Wellesley College, 2010
Submitted in partial fulfillment of the requirements for the degree of
Master of Science
4ASSACHUSETTT T
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
and the
WOODS HOLE OCEANOGRAPHIC INSTITUTION
ARCHIVES
JUNE 2012
@ 2012 Alejandra C. Ortiz. All rights reserved.
The author hereby grants to MIT and WHOI permission to reproduce and to distribute
publicly paper and electronic copies of this thesis document in whole or in part in any
medium now known or hereafter created.
I '
Signature of Author.
.... .. ....
.. .. .. .. .. .. ..
....
......
Joint Program in Marine Geology & Geophysics
Massachusetts Institute of Technology
and Woods Hole Oceanographic Institution
A
May 11, 2012
Certified by....,
......................................................
Heidi M. Nepf
Professor of Civil and Environmental Engineering
Thesis Supervisor
Accepted by.............
Rob Evans
Chair, Joint Committee for Geology & Geophysics
Woods Hole Oceanographic Institution
Accepted by...
...........................................
Heidi M. Nepf
Chair,
epartmental Committee for Graduate Students
Massachusetts Institute of Technology
2
Investigation of the Effect of a Circular Patch of Vegetation on Turbulence
Generation and Sediment Deposition Using Four Case Studies
by
Alejandra C.Ortiz
Submitted to the Department of Civil and Environmental Engineering and Woods
Hole Oceanographic Institution on May 11, 2012 in partial fulfillment of the
requirements for the degree of Master of Science in Civil and Environmental
Engineering Jointly by the Massachusetts Institute of Technology and the
Woods Hole Oceanographic Institution.
Abstract
This study describes the spatial distribution of sediment deposition in the
wake of a circular patch of model vegetation and the effect of the patch on
turbulence and mean flow. Two different types of vegetation were used along with
two different stem densities totaling four different case studies. The spatial location
of enhanced deposition correlated with the steady wake zone, which has length, L1 .
The steady wake zone only occurred downstream of the rigid emergent patches of
vegetation and was not seen downstream of the flexible submerged patches of
vegetation. The enhanced deposition occurred when both turbulence and mean
velocity was below the upstream, initial values. The enhanced deposition occurred
when the mean velocity was less than or equal to half of the initial velocity. For the
four cases studied, these parameters of low velocity and low turbulence were
primarily met within the steady wake region immediately downstream of the two
rigid emergent patches of vegetation. In all four cases, large coherent structures are
created in the flow due to the patch. Lateral vortices are formed downstream of the
patch in a von-Karman vortex street that meets at the center of the flow a distance,
Lw, downstream of the patch. For the flexible submerged cases, streamlines reattach
to the bed of the flume a distance, L,, downstream of the patch. In addition, for the
flexible submerged cases, secondary circulation is generated with flow moving
laterally away from the patch at the surface and toward the centerline of the patch
at the bed.
Thesis Supervisor: Heidi M. Nepf
Title: Professor of Civil and Environmental Engineering
3
4
Acknowledgements
First, I offer my sincerest gratitude to my advisor, Heidi Nepf, for her advice
and help with my project. She has been invaluable with her patience and expertise
on this project. I would also like to thank my advisor, Andrew Ashton, for his help
and advice on this project. I would also like to thank him for his support for this
science master.
Several students have been very generous with their support and advice over
the last year. I would like to thank Elizabeth Follett, Natasha Maas, and Mara
Orescanin. I would also like to thank Lijun Zong for her instruction and time. Finally,
I would like to thank ZB Chen for his help in the lab and with the experiments.
Lastly, I give my most sincere thanks to my family and friends for all of their
love and support. I also thank my mother for her editing and my friends for their
unstinting encouragement.
This material is based upon work supported by the National Science
Foundation under Grant Nos. EAR 0738352 and OCE 0751358. Any opinions,
findings, and conclusions or recommendations expressed in this material are those
of the authors and do not necessarily reflect the views of the National Science
Foundation
5
6
Table of Contents
CHA PT ER 1
IN T R O D U CT IO N ....................................................................................................
1.1.
BACKGROUND..............................................................................................................................................15
1.2.
O UTLINE.......................................................................................................................................................17
CH A PT ER 2
M ET H O D O LO GY ....................................................................................................
2.1.
EXPERIM ENTAL M EASUREM ENTS......................................................................................................
2.2.
DATA PROCESSING.....................................................................................................................................23
2.3.
DATA A NALYSIS..........................................................................................................................................28
CHA PT ER 3
RESU LTS ................................................................................................................
3.1.
CONTROL EXPERIM ENTS...........................................................................................................................31
3.2.
RIGID EM ERGENT VEGETATION ..............................................................................................................
13
18
18
31
33
3.2.1.
Case 1 - Rigid D ense ........................................................................................................................
36
3.2.2.
Case 2 - Rigid Sparse.......................................................................................................................
41
FLEXIBLE SUBM ERGED VEGETATION ...............................................................................................
46
3.3.
3.3.1.
Case 3 - Flexible Dense ...................................................................................................................
50
3.3.2.
Case 4 - Flexible Sparse..................................................................................................................
5 7
CH A PT ER 4
D ISCUSSIO N ...........................................................................................................
64
CHAPTER 5
CONCLUSIONS & FUTURE WORK ....................................................................
74
7
List of Figures
Figure 1-1. Conceptual plan-view diagram of the flow around a porous rigid
em ergent vegetation patch ...................................................................................................
Figure 2-1. Plan-view experiment setup in the flume. .......................................................
17
21
Figure 2-2. Diagram of use of Acoustic Doppler Velocimeter (ADV) in flume for Rigid
Em ergent vegetation patch...................................................................................................
22
Figure 2-3. Diagram of ADV in the flume for flexible submerged sparse vegetation
p a tch ...................................................................................................................................................
23
Figure 3-1. Net deposition along centerline of flume for control experiment where H
= 13.5 cm with plotted mean and standard deviation of net deposition......... 32
Figure 3-2. Net deposition along centerline of flume for control experiment where H
= 21.5 cm with plotted mean and standard deviation of net deposition.......... 33
Figure 3-3. Mean velocity and turbulence along the centerline of the flume for Case
1............................................................................................................................................................
34
Figure 3-4. Mean velocity and turbulence along the centerline of the flume for Case
2 ............................................................................................................................................................
35
Figure 3-5. Quiver plot of the flume in plan view for Case 1. ..........................................
37
Figure 3-6. Deposition and velocity along centerline of the flume for Case 1.......... 39
Figure 3-7. Lateral transects of normalized A) velocity, B) urms, and C)TKE for Case
1............................................................................................................................................................
40
Figure 3-8. Spectral analysis of velocity data taken along centerline of flume at 7 cm
d ep th fo r Case 1 .............................................................................................................................
8
41
Figure 3-9. Quiver plot of the flume in plan view for Case 2 ...........................................
42
Figure 3-10. Deposition and velocity along centerline of the flume for Case 2........... 44
Figure 3-11. Lateral transects of normalized A) velocity, B) urms, and C) TKE for
Ca se 1 .................................................................................................................................................
45
Figure 3-12. Velocity Spectra measured along centerline of patch at 7 cm depth for
Ca se 2 .................................................................................................................................................
46
Figure 3-13. Conceptual diagram of plan view of the flow around porous flexible
submerged patch of vegetation. .........................................................................................
47
Figure 3-14. Conceptual diagram of side view of the flow over submerged flexible
v e g e tatio n .........................................................................................................................................
48
Figure 3-15. Conceptual diagram of normal view of flexible submerged patch of
v e g e tatio n .........................................................................................................................................
Figure 3-16. Quiver plot of the flume in plan view for Case 3.................
48
51
Figure 3-17. Vertical-lateral quiver slices taken in y and z throughout the flume from
x = -50, 50, 100, and 400 cm, respectively for Case 3 (x/D = -1.2, 1.2, 2.4, 4.8,
a n d 9 .5 )..............................................................................................................................................
52
Figure 3-18. Deposition and velocity along centerline of the flume for Case 3........... 54
Figure 3-19. Lateral transects of normalized A) velocity, B) urms, and C) TKE for
Ca se 1.................................................................................................................................................
55
Figure 3-20. Normalized intensities of turbulence fluctuations along centerline of
flume at three depths for Case 3........................................................................................
Figure 3-21. Quiver plot of the flume in plan view for Case 3.................
9
56
58
Figure 3-22. Vertical-lateral quiver slices taken in y and z for Case 4........................
59
Figure 3-23. Deposition and velocity along centerline of the flume for Case 3........... 60
Figure 3-24. Lateral transects of normalized A) velocity, B) urms, and C) TKE for
Ca se 1.................................................................................................................................................
62
Figure 3-25. Normalized intensities of turbulence fluctuations along centerline of
flume at three depths for Case 4........................................................................................
63
Figure 4-1. Predicted sediment deposition along the centerline of the flume for each
ca se ......................................................................................................................................................
70
Figure 4-2. Horizontal velocity versus turbulence kinetic energy colored and scaled
by th e n et d ep osition ...................................................................................................................
72
Figure 4-3. Locations in the flume where the deposition is measured ......................
73
10
List of Tables
Table 1. Summary of patch parameters for the four cases and two control
experim ents w ith standard deviations..........................................................................
19
Table 2. Summary of measured flow parameters with calculated standard deviation
for rigid emergent patch of vegetation (Case 1 & 2). ...............................................
35
Table 3. Summary of measured flow parameters with calculated standard deviation
for flexible submerged patches (Case 3 & 4) with standard deviation............. 49
Table 4. Summary of peak of intensities of turbulent fluctuations for each case along
centerline of flum e with standard deviation...............................................................
66
Table 5. Summary of estimated sediment concentrations for each experiment for
entire flume with calculated standard deviations based on 10% error.......... 67
11
Nomenclature
H
x,y,z
t
Uj
ui
Ut,rms
TKE
U
Uo
Ue
U2
Lo
Li
L2
Lw
Lv
n
d
h
a
D
height of water
streamwise, lateral, and normal
directions
time
time averaged velocity components
CD
CO
drag coefficient
initial sediment concentration
S-
final sediment concentration
probability of sediment
deposition
specific weight of sediment
non-dimensional fall velocity
r
sediment diameter
Ce
p
instantaneous velocity components
intensity of turbulence fluctuations
components
turbulence kinetic energy
S
total horizontal velocity
upstream velocity
exit velocity
steady wake velocity
upstream adjustment length
steady wake length
gravity
frequency
f
fall velocity
ws
hmeas depth of measurements
m
mass of sediment deposited
concentration of sediment
C(t)
over time
bed friction coefficient
Cf
Re
Reynolds number
Greek Letters
solid volume fraction
Shield's parameter
ipb
V
kinematic viscosity
density
p
9
wake recovery length
length to maximum turbulence
vertical reattachment length
dowels per bed area
dowel diameter
height of canopy
frontal area per volume
diameter of patch
12
Chapter 1 Introduction
Biogeo morphology is the study of how feedbacks between vegetation and
Earth surface processes affect the form and shape of landscapes. It analyzes the
complex feedbacks and readjustments that exist between landforms, and physical
and biotic processes (Corenblit et al., 2007). Fluvial systems have complex
interplays between the land, the flow, and biota. The linkages in fluvial systems
between vegetation and physical processes are conceptualized in the fluvial
biogeomorphic succession model (Corenblit et al., 2007; Schnauder and Moggridge,
2009). This research aims to understand the feedbacks between aquatic plants,
flow, and sediment deposition in fluvial systems, by investigating the relative
importance of turbulence and mean flow on sediment deposition. We examine how
porous patches of vegetation affect flow conditions, and consequently change
depositional patterns.
River types can be strongly influenced by the presence of riparian vegetation.
Vegetation consolidates and stabilizes riverbanks, allowing for meandering rivers to
develop instead of braided streams (Murray and Paola, 2003; Rominger et al., 2010;
Tal and Paola, 2007). Vegetation also grows within the channel as well as along the
banks. In fluvial systems, in-channel aquatic vegetation typically exists in noncontinuous patches (Corenblit et al., 2007; Naden et al., 2006). Aquatic vegetation
modifies flow hydraulics (Schnauder and Moggridge, 2009). Vegetation found in
rivers range from emergent reeds to submerged grasses. It affects water quality by
13
nutrient uptake, decreasing turbidity, and even heavy metal sequestration
(Christiansen et al., 2000; Hendriks et al., 2008; Naden et al., 2006).
Within fluvial systems, the flow entrains and transports sediment. Alluvial
rivers transport sediment in two different methods as bed load, sediment in contact
with the bed, and suspended load, sediment independent of the bed (Church, 2006;
Dade and Friend, 1998; Engelund and Fredsoe, 1976). Typically, transport as
suspended sediment comprises 50-90% of the total sediment load in the river
(Anderson and Anderson, 2011; Dade and Friend, 1998). Any sediment carried
within the flow as suspended sediment is strongly affected by changes in flow
characteristics. Sediment deposition patterns are spatially related to flow
characteristics within a river. Usually, sediment deposition is considered dependent
on the mean flow rather than turbulence (Bos et al., 2007; Christiansen et al., 2000;
Rodrigues et al., 2006). There is controversy over the role turbulence plays in
sedimentation. Some studies claim turbulence is important for sediment deposition
while others suggest mean velocity is more important for sediment deposition
(Boyer et al., 2006; Church, 2006; Nelson et al., 1995; Williams et al., 1989).
Previous work in our lab group has focused on the spatial distribution of sediment
deposition around a patch of vegetation where the primary transport is bedload
rather than suspended load (Follett and Nepf, 2012). We specifically investigate
suspended sediment transport and deposition.
14
1.1. Background
Aquatic vegetation is viewed as beneficial in fluvial restorations because it
decreases near-bed velocity and stabilizes the sediment at the bed (Pollen and
Simon, 2005). Vegetation also provides a heterogeneous habitat by creating
different flow regimes (Kemp et al., 2000). Research has focused on the
hydrodynamics of a continuous segment of vegetation (Bos et al., 2007; Ghisalberti
and Nepf, 2006; Luhar et al., 2008; Murphy et al., 2007; Murphy et al., 2006; Peralta
et al., 2008; Zong and Nepf, 2010). In fluvial systems, vegetation is commonly found
segmented in patches (Naden et al., 2006; Sand-Jensen and Madsen, 1992;
Schnauder and Moggridge, 2009). The presence of a patch of vegetation can divert
the flow around the finite size such that there is enhanced flow locally on the edges
of the vegetation patch, possibly inhibiting the expansion of the patch (Neumeier,
2007; Temmerman et al., 2005; Vandenbruwaene et al., 2011). This biogeomorphic
feedback may limit the expansion of vegetation patches.
Previous research has emphasized the importance of different stem densities
within the patch of vegetation on the flow and feedbacks with physical processes
(Bos et al., 2007; Bouma et al., 2007; Rominger and Nepf, 2011; Schnauder and
Moggridge, 2009). The individual plants in the patch of vegetation create a canopy,
whose geometry is based on the individual plants. Given a patch of vegetation with a
characteristic diameter of plants, d, and the number of stems per bed area, n, the
frontal area per volume is a = nd. The amount of flow through the patch is based on
the density of the patch described by the flow blockage value, CDaD, such that high
15
flow blockage occurs for CDaD > 4 and low flow blockage for CDaD < 4. Cases of high
flow blockage impose different behavior on the flow characteristics than low flow
blockage patches of vegetation (Chen et al., 2012 ).
Recent work has focused on the flow behind patches of rigid emergent
vegetation (Chen et al., 2012 ; Follett and Nepf, 2012; Zong and Nepf, 2011). The
flow patterns observed in these cases differ from those for a flow behind a solid
object because of the bleed flow, or flow through the patch. For a circular patch of
vegetation of diameter, D, the flow blockage parameter is defined CDaD. Given a rigid
patch of vegetation composed of wooden dowels, a steady wake velocity region is
observed behind the patch with a constant flow U1 over a region a steady wake
region, Li (Figure 1-1). The bleed flow and subsequent steady wake region delays
the onset of the von-Karman vortex street, as visualized by Zong and Nepf (2012).
When the von-Karman vortex street forms at the centerline of the flow, there is a
peak in the turbulence production. This peak in turbulence production is located a
distance Lw from the end of the patch. After the steady wake region, the velocity
recovers in the wake recovery region for a distance, L2. This study investigates the
different regions of flow that develop from an emergent rigid and a submerged
flexible patch of vegetation and the subsequent spatial effect on sediment
deposition.
16
Rigid
Emergent
7Vegetation
O
U
Figure 1-1. Conceptual plan-view diagram of the flow around a porous rigid emergent vegetation
patch.
1.2. Outline
We focused on the effect of a single patch of vegetation (of differing rigidity
and density) on flow characteristics and sediment deposition. The research
examined the spatial distribution of sediment deposition, linking it to the spatial
changes in mean flow and turbulence. Chapter 2 provides an in-depth summary of
the different methodologies used in the experiments and subsequent data analysis.
Chapter 3 details the results from each of the four case studies of varying vegetation
type and density. The cases were divided by the type of vegetation studied and by
the density of the vegetation patch. Chapter 4 discusses the linkages between the
four cases, and, based on the data, predicts when and where enhanced sediment
deposition will occur. Finally, Chapter 5 describes the conclusions of this research
and recommendations for future work.
17
Chapter 2 Methodology
All the experiments were conducted in a flume with a patch of model
vegetation. Two types of model vegetation were used to construct circular patches,
with varying stem density. The experiments were run with model sediment. Velocity
was measured with an Acoustic Doppler Velocimeter.
2.1. Experimental Measurements
The experiments were conducted in a 16-m long re-circulating flume; the test
section is 1.2-m wide and 13-m long. A 25 hp pump was used to pump water from
the tail box to the upstream head box where a large baffle dispersed flow across the
width of the flume. The horizontal bed of the flume was covered with PVC
baseboards, perforated with a staggered array of holes, 1 cm in depth for the length
of the test section. The patch of model vegetation was constructed as a circular
staggered array. Wooden dowels with a diameter d = 6.4 mm were used for the rigid
emergent vegetation. The flexible vegetation was created using a piece of wooden
dowel (d = 6.4 mm) 1 cm in height as a stem, with six thin blades of polyethylene
film as the leaves. The model blade had a thickness of 0.2 mm, a width of 3 mm, and
a length of 13 cm. The blades were attached to the wooden dowel piece with a piece
of duct tape. The patch of vegetation had a diameter D = 42 cm. The projected
frontal area, a, is calculated as a = n*d in cm-1 where n is the number of dowels per
bed area (cm- 2 ) and d is the dowel diameter (cm). The solid volume fraction is
18
calculated for each case using
# = nrd2 /4.
For each type of vegetation (flexible and
rigid), two different stem densities were considered totaling four different cases
studies. The two different patch densities with a solid volume fraction (SVF) were
= 0.03 and
# = 0.10 for the stem region
#
of each patch (Table 1). However, for the
flexible blades, the SVF calculations were based on the number of blades of each
plant that could be visible to the flow such that the range of SVF is
and
# = 0.01 -
# = 0.04 -
0.25
0.07 for the dense and sparse case respectively. For the rigid
vegetation, the density of the patch was constant in the vertical; however, for the
flexible vegetation, the density of the patch changed with the height above the bed.
Table 1. Summary of patch parameters for the four cases and two control experiments with standard
deviations.
M-2)
Rigid Control
Rigid Dense Case 1
Rigid SparseCase 2
Flexible
Control
0.34
0.02
0.09
0.004
Flexible
Dense - Case
3
0.34 2.01 ±
0.02-0.1
0.09 0.57 ±
0.004 0.03
Flexible
Sparse- Case
4
-
a (cm-1)
CDaD
(cm-1)
H (cm)
h (cm)
UO
(cm s)
SVF
_)
0.20
0.01
-
-
13.5±
0.2
-
9.4±
0.2
8.4 ± 0.4
9.6 ± 0.5
13.5 ±
0.2
14 ± 0.2
9.4 ±.2
0.057
0.03
2.5 ± 0.1
2.5 ± 0.1
13.5
0.2
14 ± 0.2
9.4±
0.2
-
-
21.5±
0.2
-
8.1±
0.2
0.134 0.80 ±
0.006 0.04
0.0381 0.23 ±
0.002 0.01
5.5 - 34
0.3-2
1.60 - 9.7
0.08 0.5
4.2 - 25
0.2 - 1
1.20 7.2 ±
0.05 0.3
21.5 ±
0.2
10
0.2
8.1
0.2
21.5 ±
0.2
8
0.2
8.1
0.2
The two values of SVF correspond to a high flow blockage and low flow
blockage configuration. These values of SVF are representative of densities found in
19
different aquatic vegetation (Nepf, 2012). In mangrove systems, the SVF can be
quite high, 0 = 0.45 (Mazda et al., 1997). Submerged grasses, on the other hand,
tends to have lower SVF where P = 0.01 - 0.1 (Ciraolo et al., 2006).
The upstream flow velocity, Uo, was defined as the velocity measured on the
centerline at x = -100 cm (x/D = -2.4) at the highest distance above the bed. The
velocity scale, U0, was used to normalize all the velocity data. A weir at the end of the
flume controlled water depth. Two different flow depths were used to ensure
velocity measurements could be taken above the top of the flexible vegetation
canopy. For the flexible vegetation, the flow depth was H = 21.5 t 0.2 cm; in the rigid
vegetation cases, the flow depth was H = 13.5 t 0.2 cm. For the flexible vegetation,
the sparse case had a canopy height of h =8.0 t 0.2 cm; for the dense vegetation
patch, the canopy height was higher due to the greater numbers of plant blades such
that h =10.0
0.2 cm.
The coordinate system was defined with x in the streamwise direction, y
cross-stream, and z vertical depth to the bed where x = 0 at the start of the patch; y =
0 at the center of the patch; and z = 0 at the bed (Figure 2-1). The flow
characteristics were assumed to be symmetrical about the y=0 line down the center
of flume. Measurements for both deposition and velocity were taken only on one
half of the flume.
20
Vegetationbo
o o
.4
000o
O
0nth
lm.Telrearo hw h ieto
0
~
~ 2-.Pa-iwdpstoneprmn0eu
~
Figure
0r niae yte ml etnlso h e
ofte en lw.Teaprxiat loain ofsie
of The
~ loato
~
~of ththe~oriaesse
flme
~ 0
ssonb hege ros hr
n
0Fatute cente Pan-idtepstam
edgre
n of th ircularpatch
21
.
Thlagaro
sowtedicin
Velocity measurements were taken using a Nortek Vectrino acoustic Doppler
velocimeter (ADV). The sampling volume of the ADV was 6 mm across and 3 mm
high, and was located 5 cm from bottom of the instrument prongs (Figure 2-2 &
Figure 2-3). The ADV was mounted on a movable platform above the flume, which
enabled manual positioning along and across the flume with an accuracy of t 0.5 cm
in they direction and ± 1 cm in the x direction and ± 1 cm in the z direction.
Longitudinal transects were taken through the centerline of the flume from 1 meter
upstream of the edge of the vegetation patch to 7 meters after the end of the patch
(x = -2.4 - 17D). Lateral transects were also taken: upstream of the vegetation
patch, in the vegetation patch, and downstream of the vegetation patch.
H 13.5 cm
Figure 2-2. Diagram of ADV in flume for rigid emergent vegetation patch (Case 1 & 2). The grey rods
represent the rigid patch. The ADV is measuring at a depth of 7 cm above the bed (hmeas) with a total
water depth of H = 13.5cm.
22
H = 21.5 cm
z
Figure 2-3. Diagram of ADV in the flume for flexible submerged sparse vegetation patch (Case 3 & 4).
The flexible patch is represented by the bent grey arrows with the top of the canopy at h = 8 cm for
the sparse canopy, for the dense canopy h = 10 cm. The ADV is measuring at a depth of 15, 10, and 6
cm above the bed (hmeas) with a total water depth of H = 21.5 cm.
2.2. Data Processing
The ADV collected instantaneous measurements of longitudinal (u(t)),
lateral (v(t)), and vertical (w(t)) velocity at each measurement location for 240 s at a
sampling rate of 25 Hz. The instantaneous velocity components were decomposed
into the time average ( ii,vandWi), where the over-bar indicates the time averaging,
and fluctuating components (u'(t), v'(t), w'(t)) using MATLAB & Simulink Student
Version, 2011b. The intensity of the turbulent fluctuations (Urms, Vrms, Wrms) was
estimated by the root-mean-square of the fluctuating components of velocity (
, and
V
). Finally, the turbulence kinetic energy (TKE), the kinetic energy
per unit mass associated with the turbulent eddies, was calculated as the mean of
the fluctuating components of velocity such that:
23
TKE =-( u'2+v2 +w'2
2(
Spectral analysis was used to analyze trends in the turbulence energy
cascade. For given locations, a spectrum for each component of the velocity time
series was produced utilizing MATLAB's inbuilt power spectral density with Welch's
method. Given the low patch-scale Reynolds number (Re =
= 39,000) and low
V
stem-scale Reynolds number (Restem
=
u=d = 60 -320), the Strouhal number is equal
V
to 0.2 (Norberg, 1994), allowing for the calculation of the expected frequency in the
velocity spectra for both stem turbulence production and patch-sized turbulence
production,
specifically: .2
fTtem d
.2 =
or
UV
paD
(2)
U,
where fstem was the frequency associated with the turbulence produced from the
stem; and fpatch was the frequency associated with the turbulence produced from the
patch itself in the form of a von Karman vortex street. In addition, d was the size of
the stems (wooden dowels, d= 6 mm) and D was the patch diameter (D = 42 cm).
However, for a Reynolds number close to 100 (i.e. Restem = 60 for Case 1), there is a
deviation of the Strouhal number and the alternating vortices are not formed.
The deposition experiments were conducted separately from the ADV
measurements. Numbered slides were placed along the bed of the flume, as shown
in Figure 2-1. Net deposition was estimated by weighing each slide before and after
24
a deposition experiment. The slides (7.5 x 2.5 cm) were cleaned, numbered, and
weighed prior to their use in the experiments. The flume was filled to the desired
water depth, dependent on the vegetation type, with the circular patch of vegetation
in the flume. The slides were placed perpendicular to the flow direction along the
bed of the flume every 10 cm on the centerline in a longitudinal transect starting 1
meter before the patch (x/D = -2.4) and ending 6-8 meters (x/D = 14.3 - 19.0) after
the patch (Figure 2-1). The flume was filled with water before the slides were placed
to prevent the slides from being moved out of position by the infilling water.
Lateral slide transects were also placed upstream and downstream of the
vegetation patch. Depending on the density of the vegetation patch, a different
configuration of slides was placed within the patch itself. For the sparse patch (<=
0.03), the regular-sized slides were placed every 2-3 cm along the centerline of the
patch without any removal of plants. For the dense patch (#= 0.10), five small slides
(2.5x2.5 cm) were placed within the patch by removing a single plant at each
location.
Once the slides were placed, the pump was started up slowly until the initial
upstream flow velocity was reached (Uo) so that the slides would not move out of
position. Spherical glass beads (made by Potters Industry with a diameter of 12 pm,
a density of 2.5 g/cm 3, and a settling velocity of 0.01 cm/s) were used as the
sediment in the deposition experiments. A total of 650 grams of the sediment was
vigorously mixed with water in small containers before being poured into the flume
upstream of the patch. Within a minute, the sediment was well mixed in width and
25
depth across the flume. The initial concentration in the flume was Co = 105 g/m
and 75 g/m
3
3
for the rigid and flexible vegetation cases respectively. Co was
calculated by estimating the total volume of water within the flume, given the
measured dimensions of the flume, the water height in each area of the flume, and
dividing by the amount of sediment released. The flume was left to run for four
hours. At the end of four hours, the flow was slowly decreased to prevent scour and
to decrease the possibility of backwash from a sudden drop in velocity moving the
slides. Once the flow was stopped fully, the flume was drained. This entire stopping
process took around 20 minutes compared to a four-hour experiment.
The slides were then left to dry in the flume for 2-3 days until the sediment
had formed a dry white coating on the slides and the rest of the flume was dry. The
slides were carefully removed from the flume and put into a drying oven at 500 C for
2-4 hours to remove all excess moisture. The slides were reweighed to determine
the amount of sediment deposited on each slide. The net deposition was calculated
for each location by the difference in weight for each slide before and after the
experiment divided by the area of the slide.
Each deposition study was run in triplicate for each plant case (i.e. rigid
dense - Case 1, rigid sparse - Case 2, flexible dense - Case 3, and flexible sparse Case 4). The variance among triplicates at each measurement position was used as
an estimate of uncertainty for that position. In addition, for each water depthvelocity combination, a control deposition experiment was run with the flume
empty of vegetation but otherwise with the same setup (i.e. PVC baseboards
26
covering the bed and slides used to determine net deposition). The control
experiment indicated the background deposition without vegetation for the given
initial flow Uo = 9.4 t 0.2 cm/s or Uo = 8.1
0.2 cm/s and water height H = 13.5 t 0.2
cm or H = 21.5 t 0.2 cm.
The deposition data showed high variability between the replicates in the
cases of the flexible vegetation within the patch. The large variance within and
around the flexible patch was due in part to the plant blades falling onto the slides
while drying and wiping off sediment. Attempts were made to decrease this
occurrence as the flume was drained, but these were limited by concerns of
disturbing the sediment off the slides while still wet. This issue only occurred with
the flexible blades; therefore, all values that were affected by the blades were
removed from the analyses.
Mean total deposition was estimated for each of the deposition cases and the
two control experiments. The net deposition was taken from the longitudinal
transect along the centerline of the flume for each slide measurement. The net
deposition measured for each slide was then used as the net deposition for a larger
area around the slide. The area covered half the distance streamwise until the next
slide and from the center to 21 centimeters laterally (x/D = 0.5) (- 210 cm 2 ). The
sum of the net deposition from the center to 21 centimeters laterally and from 1
meter upstream of the patch to 8 meters downstream of the patch was divided by
the bed area of the flume covered by the deposited sediment. This value was then
recorded as the net mean deposition for the given experiment.
27
2.3. Data Analysis
An advective-deposition model was used to analyze the spatial deposition
patterns for each of the four vegetation cases and the two control experiments. The
model (Zong and Nepf, 2010) was used to estimate the total sediment accumulation
per unit area on the bed of the flume as a function of x (longitudinal or streamwise
distance), such that
m(x)-pw
C(t)dt
(3)
Where ws is the calculated fall velocity for the spherical glass particles (ws = 0.01
cm/s) (Madsen). C(t) is the suspended sediment concentration in the flow over time
estimated from knowing the initial concentration, based on the amount of sediment
poured into the flume and volume of water, and extrapolating the final
concentration of sediment in the flow (Ce = C(4 hours)) by extrapolating the total
amount of sediment deposited on the bed of the entire flume. This is then integrated
over the total duration of the experiment. Finally, p is a probability function of
sediment depositing in the flow based on the Engelund-Fredsoe Equation (Engelund
and Fredsoe, 1976). This equation predicts whether or not sediment will be
deposited using the probability based on the critical shear stress: as flow
decelerates, the local friction velocity, u-, decreases and the probability that
sediment will deposit increases until $ equals $cr.
The non-dimensional shields parameter is estimated from:
28
u2
=U 2
(4)
(s -1)gr
where s is the specific weight of the sediment (ps/p, = 1.25); g is gravity 981 cm/s 2 ,
r is the sediment diameter (r = 0.0012 cm); and u* (x) is the friction velocity
estimated from u. = UCf . Cf is the bed friction coefficient previously measured for
flow over the PVC boards to be 0.006 (Zong and Nepf, 2010). Uwas calculated as the
total horizontal velocity measured at each location in x such that U = Vi +V2 .The
specific sediment weight is s = 2.5. Finally,
/cr
is calculated using the modified
Shield's diagram such that P,. = .1S- 2 /1 (Madsen and Grant, 1976). S* is the nondimensional value that is a function of the fluid and sediment properties such that
S,=-r(s -1)gr where v
4v
=
0.01 cm 2 /s is the kinematic viscosity for fresh water at a
temperature of 20*C. The estimated non-dimensional lpcr= 0.25. Though, the Shield's
value can be unrealistic at very low Re* values (where the sediment size is small),
given that the glass spheres were well mixed before and were perfectly spherical,
clumping and flocculating were assumed to be minimal (Madsen; Madsen and Grant,
1976). Thus, the use of the extended Shield's parameter at low values was valid. For
$< 4cr, the probability function is set to p = 1. For 0 > 0cr, the probability that
sediment will be deposited is less than unity due to initiation of motion because the
shear stress is above the critical shear stress.
The above deposition model did not take into account a change of bed
roughness and equivalent u values within the patch. It also assumed that C(t) was a
29
linear decrease over time, and well mixed over depth and width throughout the
experiment. Visually, this did seem to be a valid assumption. After the four hours of
the experiment, the sediment was still well mixed laterally and vertically. Previous
work with this model fit the resultant curves to the actual deposition data by
varying the estimated fall velocity ws; in this study, this was not done as the model
was used purely to estimate trends in the data set (Zong and Nepf, 2010).
30
Chapter 3 Results
3.1. Control Experiments
A control deposition experiment was run for both the h = 13.5 cm (equivalent
to the rigid emergent patch of vegetation Case 1 & 2) and the h = 21.5 cm
(equivalent to the flexible submerged patch of vegetation Case 3 & 4). These two
deposition experiments were run to estimate the variability in spatial deposition
along the flume. The control for the rigid emergent cases has a mean deposition of
0.0025 ± 0.0001 g/cm 2 where the error is estimated from the variability inherent in
both the longitudinal profile along the centerline and the variability along the lateral
transects that mirrored each other (Figure 3-1). The control for the flexible plant
cases has a mean deposition of 0.0026 ± 0.0002 g/cm 2 where the error is calculated
the same as for the other control experiment (Figure 3-2). The mean net deposition
for the rigid control experiment is 0.0025 ± 0.0003 g/cm 2. The mean net deposition
for the flexible control experiment is 0.0027 ± 0.0003 g/cm 2 .
31
Rigid Control Experiment
x 10-3
2. 6-
2.5
5-
E
*
*
0)
C:2.
0
Q.
z
2.4
1:-
e Control Data
-- Mean Deposition*
--- Standard Deviation
2. 4 -
.- -- Standard Deviation*
0
-
5
10
Distance Streamwise in Flume x/D
15
20
Figure 3-1. Net deposition along centerline of flume for control experiment where H = 13.5 cm with
plotted mean and standard deviation of net deposition.
32
Flexible Control Experiment
x 10-3
4
2.75
2.7
2.65-
*
c4- 2.6
E8
c 2.55 0
0
2.5 -...............
...
_._._.._._ _....______.....
..
..............
....................
2.45 8
Control Deposition
-Mean
2.4-
of Deposition
--- Standard Deviation of Deposition
---
Standard Deviation of Deposition
2.35 -8
-
2.30
5
10
20
15
Distance Streamwise in Flume x/D
Figure 3-2. Net deposition along centerline of flume for control experiment where H
plotted mean and standard deviation of net deposition.
=
21.5 cm with
3.2. Rigid Emergent Vegetation
Case 1 and Case 2 were specifically chosen such that they fell into the high
flow blockage (CDaD = 8.4) and low flow blockage (CDaD = 2.5) cases respectively
(Table 2). Upstream of the patch, flow is affected by the patch a distance, Lo, the
upstream adjustment length, which is proportional to the diameter of the patch, D
(Figure 3-3 & Figure 3-4). Different flow regimes develop based on the flow
blockage, where the high flow blockage experiences decreased flow through the
patch itself and has very low flow, U1
-=
0.05Uo, immediately downstream of the
patch and an area of recirculation (Table 2 & Figure 3-3). The low flow blockage
case has increased flow through the patch compared to the high flow blockage case
such that the flow immediately downstream of the patch, U2 = 0.5 U, with no area of
33
recirculation (Table 2 & Figure 3-4). The area of low flow, U2, lasts for the steady
wake region, Li. Within the steady wake region, there is both low velocity and low
turbulence. The shear layers converge on the centerline of the flume at the distance,
L2, creating the von-Karman vortices. The presence of the von-Karman vortices
increases turbulence and velocity, and the peak in TKE is at a distance, Lw. The
velocity increases in the wake recovery zone, L2 , till by the end of L2 the flow has
recovered back to initial upstream velocity.
Rigid Dense
1.5
-L
LT-++ -- L 2
-
1 Control U
*~
Ux/U
0a
TKE
*
7Control
0 075
TKE/U2
Ua
*
0-4
AS;
0
p
-2
0
2
4
6
8
10
12
14
16
Distance Streamwise in Flume x/D
Figure 3-3. Mean velocity and turbulence along the centerline of the flume for Case 1. Mean velocity
normalized to U0 on primary axis. TKE normalized on secondary axis. The x-axis is streamwise
distance normalized D. The control velocity with standard deviation is plotted as the solid black line.
The control turbulence with standard deviation is plotted as the solid grey line on the secondary axis.
The different flow regimes seen in the conceptual diagram, Figure 1-1, are labeled by the parameters
L,, L1, Lw, L2 (Table 2).
34
Rigid Sparse
1,5
10-08
Control U
Ux/U
0
*Control
U
-III
-L
01
TKEQ
TKE/U2
L2
U
a
Usa
0.5
a
-1004
Lj
U,
UU
gon aa aa
LW
"%-
-5
0
I
I
I
5
10
15
20
Distance Streamwise in Flume x/D
I
Figure 3-4. Mean velocity and turbulence along the centerline of the flume for Case 2. Mean velocity
normalized to U on primary axis. TKE normalized on secondary axis. The x-axis is streamwise
distance normalized D. The control velocity with standard deviation is plotted as the solid black line.
The control turbulence with standard deviation is plotted as the solid grey line on the secondary axis.
The different flow regimes seen in the conceptual diagram, Figure 1-1, are labeled by the parameters
Lo, L1 , Lw, L2 (Table 2).
Table 2. Summary of measured flow parameters with calculated standard deviation for rigid
emergent patch of vegetation (Case 1 & 2).
Mean Total
Deposition
Rigid
Control
Rigid
Dense Case 1
Rigid
SparseCase 2
U1
L1
Lw
L2
-
UO
9.4±
0.2
-
-
4.2D
4.3D
13.5
0.2
14
0.2
9.4
0.2
0.05Uo
.06Uo
2.8D ±
0.5D
0.5D
13.5
14
0.2
9.4
0.2
0.53Uo
± .05Uo
6.6D
0.7D
8D
2D
0.5D
10.2
D±
0.7D
h
-
H
13.5
0.2
8.4
0.4
2.5
0.1
± 0.2
CDaD
35
(g/cm 2 )
0.0025 ±
0.0003
0.0022±
0.0004
0.0026±
0.0004
3.2.1. Case 1- Rigid Dense
Velocity measurements are taken at 7 cm above the bed of the flume. These
measurements are used to visualize the flow characteristics around the patch of
vegetation (Figure 3-5). The flow is strongly diverted around the patch laterally at x
= 0 - 1.5 D, and the velocity increases locally (ux = 1.6U0 ) by the diversion around
the patch. The flow is then directed back towards the center of flume where the flow
is back to initial flow (within 10% of Uo) by 4 meters from the patch (x = 9.5D, L2 =
4.3D) (Figure 3-3). In addition, measurements directly downstream of the patch
demonstrate the marked decrease in velocity. This effect of the patch on the flow
creates a zone of very low velocity known as the steady wake region, L, = 2.8D.
There is also a section of recirculation along the centerline starting at x = 3.1 - 3.8 D
from the start of the patch (Figure 3-6). The velocity measurements along the
centerline are not pointed purely in the streamwise direction due probably to
instrument position error, i.e. the ADV was not facing exactly perpendicular to flow.
36
Rigid Dense
15
1.6
1
1.4
1.2
E 0.5N
0.
0.2
-1.5
-4
-2
0
2
4
6
8
10
Distance Streamwise in Flume X/D
12
14
16
0
Figure 3-5. Quiver plot of the flume in plan view for Case 1, where the length of the arrows and the
color of the arrows indicate the horizontal velocity magnitude.. The colorbar on the right shows the
total horizontal velocity relative to the Uo. The location of the patch is shown by the black ellipsoid.
To visualize the change in velocity and deposition, data collected along the
centerline of the patch are graphed (Figure 3-6). The velocity measurements are
normalized by the upstream velocity, Uo, as calculated from the control experiments
(Table 2 & Table 3). In addition, the y-axis limits are set such that the dashed black
line is located at the measurement from the control experiments (i.e. in the rigid
control experiment, urms/Uo = 0.13 ± 0.3 cm/s). The secondary y-axis plots the mean
deposition values relative to the control mean deposition, by subtracting the mean
deposition from the local deposition. The dark gray shaded line is the measured
standard deviation from the three replicates, where the middle of the grey area
37
marks the mean value of the three replicates. The dashed black line also denotes the
zero deposition relative to the control (i.e. anything below that line is deposition
that is less relative to the control, while anything above the zero line indicates
enhanced deposition relative to the control experiment). The location of the
vegetation patch is shown by the thick black vertical lines located at x= OD & 1D.
Deposition upstream of the patch is highly variable between the three
replicates, as indicated by the high variance (Figure 3-6). Downstream of the patch,
the deposition increases relative to the control experiment for 1 meter behind the
patch (till x = 3D). From x > 3.5D, the deposition is lower than the control, and it
stays lower to the end of the measurement section (x = 21D). The decrease in
deposition, relative to the control, corresponds to the positions with an increase in
urms and TKE. The peak in TKE and urms at x = 5D corresponds to where the von-
Karman vortex street begins, Lw = 4.2D (Table 2).
38
Al.
X10
Velocity and Deposition Data Relative to Control forRigid Dense Vegetation Patch at y = 0 @ H =7cm
LStd Dev of Dense RIG Deposition Data with Control Subtracted 1.2
Rig Dense Velocity-1.
0.8 E
0.4
~
--------------
0--------
---------------
-0.4
a
-0.80
-.2 z
-3
2
7
Distance Streamwise X/D
B1.2
1
72
12
-
x 10
E
17
22
x 10
C)1.2
0 8
0.8 0-0.8gi
E
0
0.4 a
0.4"
-------------
-------
----------
~
-------
--
-0
-0.8 0705-0.8
-1.2
-3
2
12
7
Distance Streamwise XID
17
22
-1.2
0
10
15
5
Distance Streamwise X/D
20
Figure 3-6. Deposition and velocity along centerline of the flume for Case 1. The x-axis is normalized
by the patch diameter, D. The secondary y-axis is the net deposition relative to the control
experiment (g/cm 2). The location of the patch in the streamwise direction is indicated by the black
vertical lines on each graph. A) U/Uo on the primary y-axis and the mean deposition of the three
replicates with the standard deviation of the replicates indicated by the edges of the polygon fill on
the secondary y-axis. B) urms/Uo on the primary y-axis. C) TKE/u 0 2 on the primary y-axis.
The lateral velocity transects indicate the lateral extent of patch influence on
the flow(Figure 3-7). Directly downstream of the patch at x = 1.2D, flow is strongly
depressed to 0.05 U0, but a large increase in velocity to 1.5Uo is visible at the lateral
edge of the patch (x = 0.5D). At half a meter behind the patch (x = 2.4D), the lateral
transect is still similar in structure to that measured directly behind the patch. By
three meters from patch (x = 7.14D), the flow is laterally uniform. Directly
downstream of the patch, there is a peak in urms that increases strongly at 1 meter
from the patch (x = 2.4D). Even though the urms remained high along the centerline
39
of the flume after the peak at x = 6D (Figure 3-6), it is much less than the urms spikes
at x = 1.2D and 2AD.
Directly downstream of the patch, there is a spike in TKE at the lateral edge
of the patch (y = O.5D), and this elevated region of TKE moves laterally inwards
towards the center moving downstream (x = 2.4D). This is associated with the shear
layer forming at the edges of the wake and growing inward over distance (Figure
3-7). However, by three meters from the patch (x = 7.1D), the TKE is significantly
elevated over the entire lateral transect corresponding to the presence of the large
coherent turbulent structures of the von-Karman vortex street, Lw = 4.2D (Figure
1-1).
Rigid Dense
A)
2
0 Lateral Profile @ X = 50cm Z = 7 cm
0
D
D
*
* Lateral Profile @ X = 100cm Z = 7 cm
+ Lateral Profile @ X = 300cm Z = 7 cm
-- Control
1.5
*
*
*
*
+
+
+
+
*..
0
98
0.5
I
f rMau"m-
0.2
0.4
0.6
0.8
1
Distance Across Flume Laterally y/D
0.1
0.3
+
+ +
B)90.25
.- +.
-
+
+
C0.08
+
+
+
+
+
+
0.06
++
+++
D 010.
++
+
*
--
0.1
.--------4*
*
0.0
*
0.04
@6
*
*
0
*
0.02
*
*0*
0
* 0*
0.4
0.6
0.2
0.4
0.6
0.8
0
1
Distance Across Flume Laterally y/D
~.
------------------------------------------------------6
"p
0
0.2
0.8
1
Distance Across Flume Laterally y/D
Figure 3-7. Lateral transects of normalized A) velocity, B) urms, and C) TKE for Case 1. The
horizontal axis is the distance across the flume from the center of the flume (y = 0), normalized by
the patch diameter.
40
Spectral analyses of the velocity measurements taken along the centerline
indicate the varying production terms of turbulence (Figure 3-8). Upstream of the
patch of vegetation (x = -2.4D), the spectra have no distinctive peaks indicating a
lack of a specific length scale to turbulence production. Downstream of the patch (x
= 2.6D), the largest peak in Sv is observed to correspond with the turbulence
associated with the length scale of the entire patch of vegetationf= 0.05 Hz using
the upstream initial velocity. There is no peak observed in turbulence associated
with the length scale of the individual dowel stems because the stem Reynolds's
number is around 60, thus there is no vortex shedding (Norberg, 1994).
SpectralAnalysis@y= andox - -100z7
SpectralAnalysis@0
uand a
7 c
dsZ=7
SuuU
Snl()
000,00
10iS0ini
101
0
il
S
where x = -2.4D and 2.6D (A and B). The x-axes are the frequency (Hz) and the y-axes are the spectra
in cm 2/s. Each graph has two curves plotted; the black line is the spectra in the x-component (Suu)
and the grey line is the y-component (Svv). B), the vertical grey line marks the turbulence production
based on the size of the entire vegetation patch (see Methodology for calculation).
3.2.2. Case 2 - Rigid Sparse
The rigid emergent sparse vegetation patch affects the flow characteristics
for 7 meters (x = 16.8D). The flow is diverted laterally around the patch (x = 0
-
1 D),
accelerating around the outer edge (ux = 1.1UIo) (Figure 3-9). The flow is decreased
downstream of the patch; the decreased flow lasts for 6 meters from the start of the
41
patch (x = 14.2D). The magnitude of flow retardation and acceleration is less than
that for the rigid emergent dense patch of vegetation where U2 = 0.05 U0 and U =
0.5Uo in Cases 1 and 2, respectively (Table 2). However, the distance of the steady
wake zone is longer for Case 2 than Case 1 (i.e. L2 = 2.8D and L1 = 6.6D for Cases 1
and 2, respectively). In addition, the wake recovery is longer for Case 2 than Case 1
(Lz
=
4.3D and L2 = 10.2D for Cases 1 and 2, respectively). There is no recirculation
zone for Case 2 as it is a low flow blockage case (Chen et al., 2012 ; Rominger and
Nepf, 2011; Zong and Nepf, 2011).
Rigid Sparse
1.4
1.2
1
1
E 05k.V)
CA
0.8
0
-
N
0.6
Ai)
0
-0,.:
0.4
-1
-1.5'
-5
0,2
0
5
10
15
Distance Streamwise in Flume X/D
20
25
jo
Figure 3-9. Quiver plot of the flume in plan view for Case 2, where the length of the arrows and the
color of the arrows indicate the horizontal velocity magnitude. The colorbar on the right shows the
total horizontal velocity relative to the Uo. The location of the patch is shown by the black ellipsoid.
42
The deposition upstream of the patch is only slightly elevated above the
control deposition (Figure 3-10). Downstream of the patch, however, there is
enhanced deposition relative to the control deposition for 3 meters (x = 8D), which
corresponds to the steady wake region (Li = 6.6D). This trend follows the decreased
mean flow, us, and the depressed urms and TKE. After 4 meters (x = 9.5D), the
deposition is no longer elevated relative to the control, and both urms and TKE are
also elevated. The mean flow, u, does not increase back to the initial flow until
around 6-7 meters, L2 = 10.2D, (x = 14.2D). Within the patch, both the urms and TKE
are elevated. In addition, there is decreased deposition within the patch relative to
the control, and relative to the deposition immediately downstream of the patch.
The spike in urms and TKE is highest within the patch compared to the rest of the
flume (Figure 3-10 & Figure 3-11).
43
Velocity and Deposition Data Relative to Control ior Rigid Sparse Vegetation Patch at y = 0 @ H =7cm
Std Dev of Sparse RIG Deposition Data with Control
Rig Sparse Velocity
F]
A).
L
-3
12
7
Distance Streamwise X/D
2
7
12
17
12
17
22
-3
22
%1 a
Distance Strearnwise X/D
0
5
10
15
_3
20
Distance Streamwise X/D
Figure 3-10. Deposition and velocity along centerline of the flume for Case 2. The secondary y-axis is
the net deposition relative to the control experiment (g/cm 2 ). The location of the patch in the
streamwise direction is indicated by the black vertical lines on each graph. A) U/Uo on the primary yaxis and the mean deposition of the three replicates with the standard deviation of the replicates
indicated by the edges of the polygon fill on the secondary y-axis. B) urms/Uo on the primary y-axis. C)
TKE/uo2 on the primary y-axis.
Upstream of the patch, the mean flow is laterally uniform within uncertainty
of the measurements (Figure 3-11). Downstream of the patch, the flow is depressed
on the centerline (u, = O.5Uo); but elevated outside the patch wake (u, = 1.4Uo).
Moving downstream from the patch, the mean flow gradually becomes laterally
uniform until by x = 14.3D, (u, = 0.8 - 1.1 Uo). Upstream of the patch, both urms and
TKE are relatively low; it is 0.8 of the measured open channel flow from the control
experiment. Immediately downstream of the patch, there is a peak in Urms and TKE at
the lateral edge of the patch (y = 0.5D). Further downstream, Urms and TKE remain
elevated compared with both the upstream flow and the open channel flow from the
44
control experiment. In addition, while elevated overall, the TKE is not laterally
uniform; the urms is laterally uniform. Both of the values remain elevated above the
open channel flow due to initiation of the von-Karman vortex street at the center of
the flume, Lw.
Rigid Sparse
Control
* Lateral Profile @ X = -200 cm Z = 7 cm
* Lateral Profile @ X = 50 cm Z = 7 cm
2-
1.5
+ Lateral Profile @ X = 400 cm Z = 7 cm
A Lateral Profile @ X = 600 cm Z = 7 cm
0
A
A
A)
A-
+
01 *
A
A
+
*
+
4
+
*
. +
A
*
.
**
0
0.6...0.8
0.
0.2
0.4
0.6
0.25
0.03
0.2
0.025.
++
0.15
+
+
D) 0.
D
w 0.01.
~
+
+A'&
+&
A
I±+ +
+
41 A*4
A
A
S0.0
0.05
+
+
0.05
+. + +
A
DI
0.8
Distance Across Flume Laterally y/D
*~
@*
0.005
Un
0
0.2
0.4
0.6
0.8
0.2
1
Distance Across Flume Laterally y/D
0.4
0.6
0.8
1
Distance Across Flume Laterally y/D
Figure 3-11. Lateral transects of normalized A) velocity, B) urms, and C) TKE for Case 1. The x-axis is
the distance across the flume from the center of the flume (y = 0), normalized by the patch diameter.
Within the patch of vegetation and immediately downstream of the patch of
vegetation, there is a peak in the turbulence energy cascade linked to the individual
wooden dowel stem (Figure 3-12) the grey vertical line marks the predicted
frequency for the individual stems,ftem = 2.5 Hz (as calculated in Methodology). For
the sparse case, the Restem = 320, thus the predicted presence of vortices off of the
dowel is expected unlike in Case 1, where Restem
-
60. Further downstream where
there are peaks in urms and TKE, the largest peak in the power spectra is linked to the
45
von-Karman vortices created by the diameter of the patch of vegetation,fpatch = 0.04
Hz (where the vertical grey line marks the predicted frequency for the length scale
of the patch).
SpectralAnalysis@ y = and x = -1609z=8
SpectralAnalysis@ y =0 and x =23@z=8
100
-- Suu
Svv'1000
Svv1000
O
E
10
-
B).
10'.
A
iy
to-'
o2
10
Frequency (Hz,)
SpectralAnalysis@ y
1o
10
10,
Frequen
cy (Hz)
0 and x= 400@z8
t0
10,
-Pa
10
t0
10
10
to
is-
10
1
Frequency(Hz)
10
i0
Figure 3-12. Velocity Spectra measured along centerline of patch at 7 cm depth for Case 2, where x =
-4.3D, O.5D, and 9.SD (A, B, and B). The x-axes are the frequency (Hz) and the y-axes are the spectra
in cm 2/s. The black line is the spectra in the x-component (Suu) and the grey line is the y-component
(Svv); the light grey vertical line represents the predicted frequency for possible turbulence
contribution. B), the light grey vertical line marks the expected frequency for turbulence production
based on the size of a single wooden dowel. C), the vertical grey line marks the turbulence production
based on the size of the entire vegetation patch (see Methodology for calculation).
3.3. Flexible Submerged Vegetation
The flexible vegetation of a submerged patch produces a range of different
flow patterns and turbulent structures in all three dimensions. In the horizontal
46
plane, or "plan-view," the flow is diverted laterally around the patch similar to the
rigid cases, but there is no L1 or evidence for a von-Karman vortex street (Lw)
(Figure 1-1 & Figure 3-13). The wake recovery zone lasts a distance, L 2 , from the
downstream edge of the patch, after which the flow is uniform again. In the vertical
plane, or "side view," the flow is diverted over the top of the patch and reattaches to
the bed a distance Ly (Figure 3-14). In addition, there is small recirculation area
downstream of the patch. Finally, there is a secondary circulation pattern that
develops visible in the view normal to flow (Figure 3-15). Vertical vortex tubes
develop alongside the lateral patch caused by the lateral shear. The vortex tubes are
tipped forward by the mean flow shear. This creates a component of vorticity with
an axis in the streamwise direction. The resulting circulation is directed away from
the patch centerline at the free surface, and towards the patch centerline at the bed.
Flexible
Submerged:
Plan View
U+
L2
Figure 3-13. Conceptual diagram of plan view of the flow around porous flexible submerged patch of
vegetation.
47
Flexible
Submerged: Side
View
L
LF
Figure 3-14. Conceptual diagram of side view of the flow over submerged flexible vegetation.
Flexible
Submerged:
Normal View
hmeas= 15 crn..
h
hmeas
= 10 crrr-
H = 21.5 cm
~
cm
D--+
Figure 3-15. Conceptual diagram of normal view of flexible submerged patch of vegetation.
48
Fluvial systems contain both emergent vegetation and frequently submerged
vegetation. The submerged vegetation can be both flexible and rigid, however, in
this research only flexible vegetation was used for the submerged cases (Case 3 &
4). This type of model vegetation is a good mimic of grasses (Bos et al., 2007;
Folkard, 2005). Sometimes flow over flexible vegetation generates monami,
however, this was not seen in Case 3 or 4 (Nepf and Ghisalberti, 2008). There is no
generation of monami because the patch length, D, is too short for a shear layer to
develop and generate Kelvin-Helmholtz vortices (Nepf, 2012). The patch of flexible
vegetation is slightly deformed by the flow, and has a given canopy height that
differs for the two different densities (Figure 3-14 & Table 3). Previous work looked
at the hydrodynamic effect of a patch of vegetation on flow by investigating the flow
fields around the patch and the distribution of Reynolds stresses (Folkard, 2005).
However, this work had a patch that extended across the width of the entire flume.
Table 3. Summary of measured flow parameters with calculated standard deviation for flexible
submerged patches (Case 3 & 4) with standard deviation.
Flexible
Control
Flexible
Dense Case 3
Flexible
SparseCase 4
h
UO
L2
L
-
H
21.5
0.2
Mean Total
Deposition
(g/cm2)
-
8.1 ± 0.2
-
-
0.0027
0.0003
1.3 - 8.0
0.4
21.5
0.2
10.0
0.2
8.1 ± 0.2
11.4
0.5D
1.4D
+
0.5D
0.0025
0.0005
0.3
21.5
0.2
8.1 ± 0.2
12.8 ±
0.5D
CDaD
CDah
5.533.6
± 0.4
1.69.7 ±
0.1
1.5D
1.8
0.1
-
8.0 ± 0.2
49
0.5D
0.0026
0.0005
3.3.1. Case 3 - Flexible Dense
Measurements taken near the surface show the diversion of flow laterally
around the patch (Figure 3-16). The velocity is accelerated both laterally around the
patch and vertically over the top of the patch. The velocity is then slowed to half the
initial velocity a meter and a half downstream of the patch (x/D = 5), an effect which
lasts for another 2 meters. Measurements taken at mid depth are exactly at the top
of the canopy of the patch of vegetation. The flow is diverted laterally away from the
center. The velocity is slowed to half of the initial flow half a meter behind the patch
for 3 meters (x/D = 2.2 - 5). Measurements taken near the bed are 4 cm below the
top of the canopy (almost mid canopy). The flow is slightly diverted laterally away
from the center of the flume at the upstream edge of the patch. Return flow is visible
in the half meter behind the patch (x/D = 2.4). Overall, the flow is strongly decreased
to almost zero flow downstream of the patch, and then recovers slowly staying
around half of the initial flow for four meters (x = 9.5D).
50
Flexile Dense@ Depth= 15m
B),
Flextie Dense
@ Depth = 10CM
D
1~
0
E
01 L
F-
E-05'
01
005
I.'
0
5
10
'5
Distance Streamwise in FlumeXD
.1
25
-5
0
5
10
15
DistanceStreamwisein FlumeX/D
I
20
25
Flexible Dense @ Depth = 6 cm
5.I
1.2
-i
-~
--- I
I'
r= 0.5
I'
2
0,8
H
0.6
-0.5
0.4
-~-.
-1
-1.ri
-5
0
5
10
15
Distance Streamwise in Flume X/D
20
25
Figure 3-16. Quiver plot of the flume in plan view for Case 3, where the length of the arrows and the
color of the arrows indicate the horizontal velocity magnitude. The x-axis is the position streamwise
in the flume relative to the location of the patch; the y-axis is the position laterally across the flume.
The colorbar on the right shows the total horizontal velocity relative to the uo. The location of the
patch is shown by the black ellipsoid. A) quiver at depth = 15 cm. B) quiver at depth = 10 cm. C),
quiver at depth = 6 cm.
Secondary circulation is visible throughout the measured sections of the
flume (Figure 3-17). Half a meter upstream of the patch, the flow is directed away
from the patch centerline at the surface, and then returns to the center of the flume
near the bed. While the secondary circulation does seem to diminish in magnitude
51
throughout the flume to three quarters of the initial value, the flow pattern remains
visible for at least 3.5 meters behind the patch (x = 10D).
In addition to the secondary helical flow that is created, the flow is diverted
over the top of the patch, and reattaches to the bed half a meter behind the patch
(Figure 3-14). This accounts for the return flow in the near bed measurements
behind the patch. It also accounts for the flow directed towards the bed in the center
of the flume at x = 100 cm. As seen in Figure 3-16 downstream of the patch, the flow
is slowed near the bed, and then directed back towards the patch.
0.
C
E
2
Sx
0
I
=100 cm, x/D=21 38
-1
n
0
-0.5
0.5
1
05
1
1
x = 200 cm, x/D =" 476
-0.5
-1
21-
0
0.5
1
2
0,06
0.04
0M
= 400 cm, x/D = 912
-1
-0.5
0
0.5
1
Distance Laterally Across Flume y/D
Figure 3-17. Vertical-lateral quiver slices taken in y and z throughout the flume from x = -50, 50,
100, and 400 cm, respectively for Case 3 (x/D = -1.2, 1.2, 2.4, 4.8, and 9.5). The length of the arrows
and the color of the arrows indicate the horizontal velocity magnitude. The x-axis is the position
laterally across the flume; the y-axis is the depth above the bed flume. The colorbar on the right
shows the total horizontal velocity relative to the Uo.
Velocity is accelerated over the top of the patch near the surface (Figure
3-18). Downstream of the patch, flow is decreased to at least half of the initial
52
velocity for all three depths. Within four meters (x = 9.5D), the flow recovers back to
the initial velocity. Mean flow measurements taken near the bed show highly
decreased flow (almost zero) that recovers quickly to half of the initial velocity
within one meter (2.4D). Both ums and TKE have peaks immediately downstream of
the patch, with a smaller peak above the patch. The deposition upstream of the
patch has a large standard deviation compared to the standard deviation for the rest
of the transect. The area of large standard deviation of net deposition corresponds
to the upstream flow adjustment length scale, Lo. Downstream of the patch, the
deposition is decreased relative to the control experiment. Within one meter from
the end of the patch, deposition increases slightly and stays relatively constant, but
below the control experiment.
53
A).
=1Std
Velocity and Deposition Data Relative to Control for Flexible Dense Vegetation Patch at y = 0
Dev of Dense RIG Depo Data with Control Suib
Flex Dense Velocity Depth = 15
Flex Dense Velocity Depth =10
Flex Dense Velocity Depth = 6
Disanc
Ftlrnie
XDeneVlct
-3
1
Distance Streamwise X/D
x 10
-1.2
-0.8
0,4
-0.48
et
9 5
z
13
-
17
-1.2
-1
0.4
-0A
-0.4
-04
Distance Streamnwise X/D
Distance Streamnwise XJD
Figure 3-18. Deposition and velocity along centerline of the flume for Case 3. The x-axis is the
streamwise position along the flume normalized by the patch diameter, D. The secondary y-axis is the
net deposition relative to the control experiment (g/cm 2). The location of the patch in the streamwise
direction is indicated by the black vertical lines on each graph. A) U/Uo on the primary y-axis at three
depths and the mean deposition of the three replicates with the standard deviation of the replicates
indicated by the edges of the polygon fill on the secondary y-axis. B) urms/Uo on the primary y-axis at
three depths. C) TKE/u 0 2 on the primary y-axis at three depths.
The lateral transect taken upstream of the patch indicates that the flow is
relatively uniform across the flume width (Figure 3-19). Immediately behind the
patch, the flow is depressed very strongly to almost zero, but increases to one and
half times the initial flow moving laterally away from the center of the patch. Within
4 meters (x/D = 9.5), the flow is almost uniform laterally. Both Urms and TKE show
similar trends to each other. They are uniform laterally upstream of the patch.
Behind the patch, there is damping due to the patch with a peak at the edge of the
patch from the local shear due to the velocity gradient at the lateral edge of the
54
patch. There is a large peak in both urms and TKE half a meter behind the patch (x =
2.4D). This peak, strongly pronounced in TKE, is possibly due to the streamlines that
flow over the patch and reconnect to the bed. By four meters from the patch (x/D =
9.5), all the flow parameters are nearly uniform laterally across the width of the
flume
Flexible Dense
Lateral Profile @ X = -50cm Z = 6 cm
2 _
* Lateral Profile @ X = 50cm Z = 6 cm
A
Lateral Profile @ X = 100cm Z = 6 cm
Lateral Profile @ X = 400cm Z = 6 cm
1.5
- -Control Data
0
0.5
C
0
0.2
0.4
0.6
0.8
1
Distance Across Flume Laterally y/D
0.1
0.3
0.08
0.25
A
0.2
*o
0
E
0
*
0
*
A
D 0.00.04
0.1
0.05
0
4\
o0.06
b
.0
A
*
4
A
*
.
*
0.2
A
C
0.04
*
0.4
0.6
0.8
1
0
Distance Across Flume Laterally y/D
0.2
0.4
0.6
0.8
1
Distance Across Flume Laterally y/D
Figure 3-19. Lateral transects of normalized A) velocity, B) urms, and C) TKE for Case 1. The x-axis is
the distance across the flume from the center of the flume (y = 0), normalized by the patch diameter.
The intensity of turbulence fluctuations along the centerline of the flume has
a peak in all three components half a meter downstream of the end of the patch (x =
2.4D) recorded at all three depths (Figure 3-20). This distance is the vertical
reattachment length, Lv = 1.4D, where the flow is diverted over the top of the canopy
reattaches to the bed (Figure 3-14). For flow over a submerged cube, the vertical
reattachment length, Ly, is 1.5-2.2D (Hussein and Martinuzzi, 1996; Ratnam and
55
Vengadesan, 2007). However, for a submerged hemisphere, the vertical
reattachment length, Lv, is smaller around 0.6 - 0.75D (Savory and Toy, 1986). Flow
over a submerged patch of flexible vegetation of more than twice the patch diameter
in this research, D = 1 m, has a vertical reattachment length, L, = 1.4D (Folkard,
2005). The measured vertical reattachment length, L, = 1.4D, agrees with previous
research.
Flexible Dense
0.
I
--- Control Data
0.4|-
Depth
=
15 cm
Depth = 10 cm
A Depth = 6 cm
Do0.3 1D 0.2
AA
AD
=
0.11
5
0
20
A
0.25
D
I
15
Distance Streamwise in Flume x/D
0.3
0
I
10
0
0.2
*A
E
0.15
0.
15
0.0
0.1
0.05
0
-25
0
5
10
15
Distance Streamwise in Flume x/D
200
5
10
15
Distance Streamwise in Flume x/D
20
Figure 3-20. Normalized intensities of turbulence fluctuations along centerline of flume at three
depths for Case 3. The x-axis is the distance streamwise normalized by the patch diameter; the y-axes
are the intensity of turbulence fluctuations normalized by the upstream velocity. The solid vertical
black lines indicate the patch location. The control value for a given fluctuation is the dashed black
line.
56
3.3.2. Case 4 - Flexible Sparse
Measurements taken at 15 cm above the bed are 7 cm above the top of the
canopy of the flexible sparse vegetation (Figure 3-21). The flow is diverted away
from the center for 4 meters behind the patch (x/D = 9.5); there is acceleration on
the lateral edges of the patch. Measurements taken 10 cm above the bed are 2 cm
above the top of the canopy of the flexible sparse vegetation. The flow is reduced to
three quarters of the initial velocity 1 meter downstream of the patch and
continuing for 2 meters (x/D = 2.2 - 4.8). At a depth of 6 cm above the bed,
measurements are taken 2 cm below the top of the canopy. The flow is primarily
directed towards the center of the flume for four meters behind the patch (x/D =
9.5). The velocity is significantly slowed immediately downstream of the patch to
almost zero, and remains decreased at half of the initial flow for 4 meters (x/D =
9.5).
57
A
FlIexleSparm Depth-
2 B)
15OM
a
Flexible
Sparse @Depth= 10cm
05
0
S
tI
u
5
DoIslane
Strears on FloeeX/S
20
-5
0
S
IC
Olstane SueamwiseinFlme X/I
20
Flexible Sparse @ Depth= 6 cm
1.2
C)
1
E 0.5
0.8
2
0
ZZ4U
0.6
-0.5
.2
-5
0
5
10
15
Distance Strearnwise
in FlumeX/D
20
-J
25
J
0
0
Figure 3-21. Quiver plot of the flume in plan view for Case 3, where the length of the arrows and the
color of the arrows indicate the horizontal velocity magnitude. The x-axis is the position streamwise
in the flume relative to the location of the patch; the y-axis is the position laterally across the flume.
The colorbar on the right shows the total horizontal velocity relative to the uo. The location of the
patch is shown by the black ellipsoid. A) quiver at depth = 15 cm. B) quiver at depth = 10 cm. C),
quiver at depth = 6 cm.
Vertical quiver slices taken throughout the flume highlight the secondary
flow circulation (Figure 3-22). Immediately before the start of the patch, the flow is
diverted above and over the patch. Secondary circulation is seen in the flow directed
away from the centerline at the free surface and back towards the center of the
flume at the bed. Behind the patch, the secondary circulation is still visible with the
same pattern of flow away from the centerline at the surface and back towards the
58
center at the bed. By 4 meters from the patch, the secondary circulation is no longer
present where the velocity orthogonal to flow is more than half the values upstream
of the patch.
-1
-0.5
0
0.5
1
20.05
t0
0
-0.5
0
0.5
1
2
C0.1
2--
I.021
S1210011
-1
-0.5
0
0 .5
1
Distance Laterally Across Flume y/D
Figure 3-22. Vertical-lateral quiver slices taken in y and z for Case 4 throughout the flume from x = 0,
50, 100, and 400 cm, respectively (x/D = 0, 1.2, 2.4, and 9.5). The length of the arrows and the color of
the arrows indicate the horizontal velocity magnitude. The x-axis is the position laterally across the
flume; the y-axis is the depth above the bed flume in centimeters. The colorbar on the right shows the
total horizontal velocity relative to the Uo. The black rectangle is the patch of vegetation.
The deposition pattern along the centerline of the flume is highly variable in
front of the patch, but appears to be equivalent to the control experiment (Figure
3-23). Downstream of the patch, the mean deposition is below the deposition from
the control experiment but still within standard deviation of the control experiment
59
for the length of the transect. Velocity measurements taken at three depths along
the centerline highlight the overall lack of change in velocity. Directly downstream
of the patch, the flow at the bed is reduced to less than a quarter of the initial flow,
but it doubles within a meter. Within 7D, flow is recovered to initial flow. Both the
urms and TKE have the highest peak above the patch, and a secondary peak in all
three depths 0.5 meters behind the patch.
Velocity and Deposition Data Relative to Control for Flexible Sparse Vegetation Patch at y = 0
Si8dDev of Sparse RIG Deposition Daa with Control Subtracted
X 10
-1 2
Flex Spairse Velocity Depth = 15
lex sparse Velocity Depth = 10
SFlex Spaume Velocity Depth = 6
-8
-0
~~~~
I~
3
1
~~
q.....sa..~-
.. ..
5
9
DUstance Streamwtse X/D
13
21
17
x 10
X 10
1.825
081,2
1A00
wit,
-1.2
-A2
-3
1
5
9
13
Distance Streamwise X/D
17
21
-3
5
9
13
Distance Streamnwise X/D
17
21
Figure 3-23. Deposition and velocity along centerline of the flume for Case 3. The x-axis is the
streamwise position along the flume normalized by the patch diameter, D. The secondary y-axis is the
net deposition relative to the control experiment (g/cm 2 ). The black vertical lines on each graph
indicate the location of the patch in the streamwise direction. A) U/Uo on the primary y-axis at three
depths and the mean deposition of the three replicates with the standard deviation of the replicates
indicated by the edges of the polygon fill on the secondary y-axis. B) urms/Uoon the primary y-axis at
three depths. C) TKE/u? on the primary y-axis at three depths.
Lateral velocity transects taken near the bed have the largest variability
throughout the flume. Upstream of the patch, the mean flow is uniform laterally
60
(Figure 3-24). Downstream of the patch, the mean flow is depressed directly behind
the middle of the patch, but increases moving laterally. Further downstream behind
the patch, the mean flow increases back to uniform in the lateral, such that by 4
meters from the patch flow is uniform. There is relatively little change laterally in
the urms throughout the flume for each transect. The peak in the urms directly behind
the patch is due to the shear that develops in the velocity difference at that transect
between the depressed mean flow behind the patch and the flow increasing
laterally.
There is the peak in TKE directly downstream of the patch from the
contribution of the peak in urms. One meter from the patch, the TKE is elevated
behind the patch overall and decreases moving laterally. This contribution might
come from the vertical flow component that is seen in Figure 3-15. This indicates
the presence of a large vertical structure of flow over the patch that returns to the
bed of the flume about 0.5 meters behind the patch. Overall, TKE is elevated
compared to the control experiment where TKE/uo2 = 0.015 (increasing laterally to
0.02).
61
2-
A)
Control Data
ALateral Profile @ X = -50cm Z = 6 cm
* Lateral Profile @ X = 50cm Z = 6 cm
A Lateral Profile @ X = 100cm Z = 6 cm
0 Lateral Profile @ X = 400cm Z = 6 cm
1.5
A
0A-
0
B).0
Bf0.3
0.25
0.2
0.4
0.6
0.8
1
Distance Across Flume Laterally y/D
Ic'.
*
A
0.2
0.06
*
0.
0.0
-
0.05
0
0
0.2
0.4
0.6
0.8
1
Distance Across Flume Laterally y/D
0
0
0.2
0.4
0.6
0.8
1
Distance Across Flume Laterally y/D
Figure 3-24. Lateral transects of normalized A) velocity, B) urms, and C) TKE for Case 1. The x-axis is
the distance across the flume from the center of the flume (y = 0), normalized by the patch diameter.
The intensity of turbulence fluctuations along the centerline of the flume has
a peak in all three components half a meter downstream of the end of the patch (x =
2.4D) recorded at all three depths (Figure 3-25). This distance is the vertical
reattachment length, Ly, where the flow that is diverted over the top of the canopy
reattaches to the bed. The measured vertical reattachment length (Lv = 1.5D) agrees
with previous research (Folkard, 2005; Manhart, 1998; Ratnam and Vengadesan,
2007; Savory and Toy, 1986). There is a slight increase in the measured Lv, for Case
4 compared to Case 3, which is probably due to the increased flow through the
62
sparse patch (Case 4) than through the dense patch (Case 3). This would be similar
to the effect of the bleed flow delaying the formation of the von-Karman vortex
street with the emergent patches of vegetation (Case 1 & 2) (Zong and Nepf, 2011).
0.5,--- Control Data
e Depth = 15 cm
a Depth = 10 cm
A Depth = 6 cm
0.40
0
0.31-
U,
04 ....
J___
AA
S
A
0.1
0
-5
5
A.
A
10
A
A
15
Distance Streamwise, in Flume x/D
0.251
A
4
20
0.12
A
0.2
0.11
A
Al
A
k
$
> 0.1
A
0
*
* A
-,-------
U)
4,
0.081
0.1
4
S
-----------------------
4--4--~---
0.05
44A
So.
.
*A
S
0.1
S5
1.
0
-
5
10
15
Distance Streamwise in Flume x/D
20
0
5
10
15
Distance Streamwise in Flume x/D
20
Figure 3-25. Normalized intensities of turbulence fluctuations along centerline of flume at three
depths for Case 4. The x-axis is the distance streamwise normalized by the patch diameter; the y-axes
are the intensity of turbulence fluctuations normalized by the upstream velocity. The solid vertical
black lines indicate the patch location. The control value for a given fluctuation is the horizontal
dashed black line.
63
Chapter 4 Discussion
The rigid emergent patch of vegetation affects the flow and subsequent
sediment deposition differently depending on the density of the patch. Downstream
of the dense patch, Case 1, the steady wake flow, U1 , is 2% of the initial flow, U, and
lasts for Li = 2.8D from the end of the patch (Figure 3-3 & Table 2). Downstream of
the sparse patch, Case 2, the steady wake flow is U1 , is 50% of the initial flow, U0, and
lasts for Li = 6.6D from the patch (Figure 3-4 & Table 2). Deposition is increased
relative to the control experiment over the steady wake region, L1, for both the
dense and sparse patch (Figure 3-6 & Figure 3-10). In the dense patch (Case 1), the
wake recovery is L2 = 4.3D, but for the sparse patch (Case 2), L2 = 10.2D (Table 2).
The length until the maximum turbulence, Lw, is very different for the two cases, Lw
= 4.2D for Case 1 and L2 = 8D for Case 2 (Table 2). The von-Karman vortex street
converges on the centerline at this distance L,.
The flexible submerged patch of vegetation has a very different affect on the
flow pattern with little difference between the different densities. There is no steady
wake region downstream from the patch, Li = 0 (Figure 3-13, Figure 3-16, and
Figure 3-2 1). Instead, the wake recovery region is L2 = 11.4D for Case 3 and L2 =
12.8D for Case 4 (Table 3). In addition, the streamlines that were diverted over the
patch upstream of the patch re-attach to the bed at Lu =1.4D Case 3 and L, =1.5D
Case 4 (Table 3). For both flexible cases (Case 3 & 4), the deposition remains near
64
constant throughout the flume within the standard deviation of the control
experiment (Figure 3-18 & Figure 3-23).
For all four cases, there is a location of maximum fluctuation of turbulence
(the root mean square variables), which corresponds to the presence of a large-scale
coherent vortex. These coherent turbulent structures vary in formation. For the
rigid experiments (Case 1 & 2), the coherent turbulence structure is the von-Karman
vortex street (Figure 1-1) (Zong and Nepf, 2011). For the flexible experiments (Case
3 & 4), the coherent structure is the reattachment of the streamline that flows over
the top of the submerged canopy (Figure 3-14) (Hussein and Martinuzzi, 1996;
Ratnam and Vengadesan, 2007; Tal and Paola, 2007). For both the rigid emergent
and flexible submerged cases, the maximum value of fluctuations (7.7Vrmso for Case 1
and 3 Vrmso for Case 3) in turbulence occurs for the dense experiment (Case 1 & 3)
compared to the sparse experiments (Case 2 & 4) (Table 4). The reason for the
maximum occurring in the two different dense cases is because the sparser the
patch is, the lower the flow blockage, and the larger the bleed flow through the
patch itself. The bleed flow delays the onset of the coherent turbulence structures:
LW = 8D for Case 2 (almost twice the distance for the dense experiment, Case 1, Lw =
4.2D) and Ly = 1.5D for Case 4 (Table 2 & Table 3). In addition, the bleed through
effect decreases the magnitude of the turbulence, the peaks in all three components
of the intensity of turbulence fluctuations is always larger for the dense experiments
than for the sparse experiments (Table 4).
65
Table 4. Summary of peak of intensities of turbulent fluctuations for each case along centerline of
flume with standard deviation.
Peak
Locus
of
Peak
Above
Control
(cm/s)
-
-
Urms
Rigid
Peak
Locus
of
Peak
Above
Control
(cm/s)
-
0.6 ±0.31-
Vrms
Peak
Locus
of
Peak
Above
Control
-
(cm/s)
-
-
-
0.5 ±0.3
-
-
Wrms
1.3
Control
0.3
Rigid
Dense Case 1
3.0
0.3
Rigid
Sparse -
1.3
-
Lw
2.4Urmso
4.7 ±0.3
L
7.7Vrmso
1.0± 0.3
L
2.0Wmso
Lw
Urmso
1.4 ±0.3
Lw
2.4Vmso
0.6± 0.3
Lw
1.7Wrmso
0.9± 0.3
-
-
0.5 ±0.3
-
Case 2
0.3
Flexible
1.4±
Control
0.3
-
-
Flexible
DenseCase 3
3.4
0.3
L,
2.4Urmso
2.7
0. 3
L,
3.0 Vrmso
1.0 ± 0.3
L
2.OWrmso
Flexible
Sparse -
2.2
L,
1 1.5Umso
1.7
0.3
Lv
I 1.9Vrmso
0.8 ± 0.3
L,
1.6 Wrmso
Case 4
0.3
j
The estimated change in suspended sediment concentration was calculated
for each experiment, enabling the calculation of the percent of sediment deposited
(Table 5). Based on these values, both the control experiments have enhanced
sediment deposition for the entire flume compared to the total sediment deposited
for all four cases. Overall, the trends inherent in this calculation matches the mean
total deposition calculated for each experiment and the controls as described in
Data Processing (Table 2 & Table 3). The rigid sparse experiment (Case 2) has the
least net deposition, the flexible dense experiment (Case 3) has the most net
deposition. In both calculations, the control experiments have almost the same net
66
deposition for the entire flume but are enhanced slightly compared to the
experiments with a patch of vegetation. Given the amount of error in these
extrapolation calculations, the total net deposition for the reach of the experiment is
unaffected by the presence of a patch of vegetation, rather it is merely redistributed
in location. This result matches experiments done with similar patches looking at
bedload sediment transport (Follett and Nepf, 2012).
Table 5. Summary of estimated sediment concentrations for each experiment for entire flume with
calculated standard deviations based on 10% error.
CO
(g/m
Percent
Deposited
Ce
3
)
(g/m
3
)
%
Rigid Control
105± 10
30±3
71± 7
Rigid Dense Case 1
105 ±10
45
5
57± 4
Rigid SparseCase 2
105± 10
35 ±4
67± 5
77 ±7
18 ±2
77± 4
77 ±7
25 ±3
67± 3
77 ±7
27 ±3
65± 3
Flexible Control
Flexible Dense Case 3
Flexible SparseCase 4
These calculations are used in a basic sediment transport model. Using an
advective-settling model, deposition is predicted along the centerline of the flume
and is compared to the experimental deposition for all four cases (Zong and Nepf,
2010). First order trends are compared between the modeled and actual sediment.
When the mean bed stress is less than the critical shear stress, the probability of
deposition maxes out, p = 1. The areas of constant deposition indicate areas where
67
the local velocity is low and producing low local bed shear stress. If the critical shear
stress was shifted, then the values of p would change accordingly to unity more
often (if critical shear stress increased) or less than unity for increasing distance (if
critical shear stress decreased).
For Case 1, the experimental data show elevated deposition upstream of the
vegetation patch, and a peak in deposition immediately after the patch that
remained elevated relative to the control for almost a meter (Figure 4-1). The
deposition is decreased, and stays lower than the control for the rest of the flume.
The patterns visible in the model, however, are different in parts. There is increasing
sediment deposition predicted before the patch, net deposition above the modeled
control deposition consistent with the actual trend. The maximum of deposition is
predicted downstream of the patch, but continues for an extra 2 meters before the
sediment deposition decreased significantly. Moreover, according to the modeled
deposition for Case 1, modeled deposition remains much higher than the predicted
deposition for the control experiment. Only after x = 10D does the modeled
deposition for Case 1 go below the modeled deposition for the control experiment.
This is in contrast to the trend in the actual data, where from x > 3D, the actual
deposition for Case 1 is less than the deposition for the control.
For Case 2, the experimental data show elevated deposition upstream of the
vegetation patch. The lowest deposition is within the patch. There is a peak in
deposition after the patch that remains elevated relative to the control for almost 4
meters (Figure 4-1). The deposition decreases and stays near the control, or just
68
below, for the rest of the flume. There is low sediment deposition predicted before
the patch, but it is elevated relative to the modeled control, which is consistent with
the experimental data. The maximum deposition is predicted for the patch, but it
continues for an extra 3 meters (x = 17.1D) before the sediment deposition is slowly
decreased. Moreover, the predicted deposition for Case 2 remains elevated above
the predicted deposition for the control experiment for the entire length of the
flume due to diminished velocity for x/D = 14 downstream of the patch. On the
other hand, the actual deposition results fluctuate above and below the control
deposition.
For Case 3, the experimental data show a decreasing deposition approaching
the patch of vegetation upstream (Figure 4-1). Immediately downstream of the
patch, there is decreased deposition, and it remains relatively uniform for the
remainder of the patch. For Case 4, the experimental data demonstrate variable
deposition before the vegetation patch (Figure 4-1). The deposition remains
relatively uniform for the remainder of the patch, except for a small dip towards the
end of the flume. For both Cases 3 & 4, the model predicts uniform deposition over
the entire length of the flume. This is because the measured flow characteristics do
not exceed the critical shear stress (0cr = 0.23). The modeled deposition for Case 3
remains at the modeled deposition for the control experiment, similar the actual
experimental data. The modeled deposition for Case 4 remains almost equal to the
modeled deposition for the control experiment, just slightly below the modeled
control deposition. The model predicts constant deposition because it only accounts
69
for changes in local bed stress based on the local mean flow; there is no dependence
on turbulence. The differences between the trends observed in the modeled and
experimental data indicate that deposition should not be solely dependant on the
local bed shear stress.
x 10 10-
X 103
10
CU
a
C8
) 8
Control Deposition Data
Control Depo Data
-Modeled
R Original Deposition Data
Modeled Depo Data
a)
6
Rigid Dense
6 - Rigid Sparse
C
4
2S4-
0
U2
0--5
0
1
0
5
10
15
Distance Streamwise in Flume x/D
20
0
0
5
10
15
Distance Streamwise in Flume x/D
20
0-3
10
CU
a)86i
0
C
CU
-0
a
Flexible Sparse
Flexible Dense
EL4
4
(0
0
S*"-I
2
a-
5-5
0
5
10
15
Distance Streamwise in Flume x/D
20
0-5
0
I
i
15
5
10
Distance Streamwise in Flume x/D
I
20
Figure 4-1. Predicted sediment deposition along the centerline of the flume for each case given the
measured flow characteristics using an advective settling model (Zong and Nepf, 2010). The x-axis is
streamwise distance along the flume; the y-axis is the net deposition per unit bed area.
By considering both the total horizontal velocity and the TKE for each case,
interesting trends are revealed in the experiments. The flow measurements can be
categorized into four areas based on the flow characteristics relative to control
measurements (Figure 4-2). The four quadrants are: high mean velocity and high
70
TKE (upper right quadrant); high mean velocity and low TKE (lower right
quadrant); low mean velocity and low TKE (lower left quadrant); and low mean
velocity and high TKE (upper left quadrant). The data are colored by the significant
deposition at each location.
The rigid dense patch, Case 1, has the largest variability in measured mean
velocity with the TKE reaching a maximum of 2Uo and 0.2TKEo. The rigid sparse
patch, Case 2, has a relatively restricted range of values for the horizontal velocity
and TKE, ranging from 0.5Uo to 1.4Uo and zero TKEo to 0.05TKEo. The flexible
dense patch, Case 3, has a wide range in TKE from 0.01TKEo to 0.15TKEo, and a
small range in horizontal velocity from 0.8Uo to 1.4Uo. The flexible sparse patch,
Case 4, is clustered around the measured control values, with a small range similar
to Case 3 except the range in TKE is smaller from 0.015TKEo to 0.1TKEo.
Overall, for all the four cases, there is little enhanced deposition relative to
the control experiments, only for Case 1 & 2 is there enhanced deposition, which is
enhanced for less than 25% of the data points (Figure 4-2). The rigid dense patch,
Case 1, has the largest amount of deposition; the majority of this deposition occurs
in quadrant III, where both TKE and horizontal velocity are below the initial values
(Figure 4-2). The rigid sparse patch has enhanced deposition also in quadrant III.
The flexible patches of both densities have no enhanced deposition relative to the
control experiment. Overall, enhanced deposition appears to occur when U s 0.5Uo
and when TKE < TKEO.
71
0.2
0.2 -
~~
Deposition < Control
Ntn
~
_ti
n
2
1/_2
e
i5'~~~
a-
Depostion4 Control
k
1
0.22-Net
.
Deposition > Control
3
015 -
eposition
i'~J~iii~tl
Deposition < Control
Depositn
+
=
(g/cm
+
Control
RigidDense
0
RigidSparse
1
.
; 0 0.1
01
1 ..
005
0.05-
0
0.2
0.4
0.2
0.6
0,8
1
1,2
Total Horizontal VelocityAJo
16
14
1,8
2
0
0.2
0.4
Deposition < Control
Deposition 4;Control
0
0.05
16
1,8
2
Deposition = C ntrol
Deposition > Control
Deposition > Control 05
F0
FlexibleDense
01.
1.4
0.6
0,8
1
1.2
Total Horizontal Velocity/Uo
Net Deposition (q/cm2
0,2.
Net Deposit+O (g/cm)
Caposition < Control
0. 15
Deposition > Control
I
015
3
Flexible Sparse
0.1
I0.05
Of
A
-----L-0
0
0.2
0.4
-
06
0.8
1
1.2
TotalHorizontal Velocity/Uo
1.4
1.6
18
2
0
0.2
0.4
0-6
008
1
1.2
1.4
Total Horizontal Velocity/Uo
1-6
18
Figure 4-2. Horizontal velocity versus turbulence kinetic energy colored and scaled by the net
deposition. The x-axis is total horizontal velocity relative to initial velocity; the y-axis is TKE/U 2 for
each graph. The points on each graph are colored and sized by the net deposition relative to the
control experiment (where deposition is either greater than the control experiment, less than the
control experiment, or within the standard deviation of the control experiment). The dashed black
lines are the flow measurements from the control experiment.
The location within the flume of the enhanced deposition fits into a specific
spatial pattern (Figure 4-3). The enhanced deposition occurs almost entirely in the
Li region, the steady wake region. It is in this region that both velocity and
turbulence are depressed, relative to the open channel control. The flexible
vegetation patch has no steady wake region downstream of the patch, Li = 0. This
would explain why there is no enhanced deposition in the flexible submerged
patches.
72
2
Net Deposition (gkm')
1
Deposition < Control Deposition = Control Deposition > Control
Depositon <Control
Deposition = Control
Rigid Dense
Significant Deposition
o
CO
( 0.5
1 05
0
0
0
Poition Stream e x/D
Net D~eposition (gFICMP
1
15
20
0
15
20
Deposition (g)
Deposition = Control Deposition > Control
1Flexible
Posion Streamwls'e x/D
1.5
NefNet
3epostion < Control
Q
Deposition> Control
Rigid Sparse
Significant Deposition
Deposition < Control Deposition = Control Deposition > Control
Dense
Significant Deposition
Q
S
0,5
0C*
Flexible Sparse
Significant Deposition
0.5.
CC
0
5
10
Position Streamwise x/D
15
20
0
5
10
Position Streamwise x/D
16
20
Figure 4-3. Locations in the flume where the deposition is measured, colored by significant
deposition relative to the control position where deposition is either greater than the control
experiment, less than the control experiment, or within the standard deviation of the control
experiment). The graphs are the plan view half of the flume, with the x and y-axis the streamwise and
lateral position normalized by the diameter of the patch. The location of the patch is indicated by the
semicircle.
73
Chapter 5 Conclusions & Future Work
Enhanced sediment deposition occurs primarily in the steady wake region
downstream of the patch of vegetation. In this region, both mean velocity and
turbulence are depressed relative to the open channel flow. In fact, for enhanced
deposition to occur, mean velocity has to be less than or equal to half the open
channel velocity, and turbulence must be less than or equal to the free stream
turbulence. The patches comprised of the rigid emergent plants have a steady wake
region immediately downstream of the patch where the mean flow and the
turbulence satisfy these requirements. However, the patches comprised of the
flexible submerged vegetation have no steady wake region downstream of the
patch. In addition, there are very few locations where turbulence and mean velocity
fall below the suggested requirements for enhanced deposition. Thus, it makes
sense that this is an overall lack of enhanced deposition for the flexible cases.
When the total deposition is extrapolated for the reach of the flume, there
appears to be no net enhanced deposition relative to the control experiments. The
presence of a patch of vegetation merely redistributes sediment around the flume.
There are local changes in net deposition relative to the control, where the steady
wake region has enhanced deposition. But on the larger scale of the reach of the
flume, there is no net enhanced deposition. The local enhanced deposition in the
steady wake region agrees with previous research. In the field during the
preliminary stages of vegetation colonization, vegetation is often found in a circular
74
patches (Sand-Jensen and Madsen, 1992). But over time, these patches have been
shown to grow predominantly in the downstream direction (Sand-Jensen and
Madsen, 1992; Schnauder and Moggridge, 2009). Since suspended sediment
typically contains fine sediment especially organics, the enhanced deposition in the
steady wake region would be preferential to fine rather than coarse sediment. This
project supports the conclusion that patches experiencing a steady wake region will
preferentially deposit sediment in that region enabling easier colonization because
of the decreased flow, decreased turbulence, and increased deposition of fine
sediment.
Increasing grain size would lower the critical shear stress value to a
minimum at medium grained sand (d = 0.3 mm) and then increase the critical shear
value to
cr
= 0.065 (Julien, 2010). Decreasing the
cr value
would mean it is easier
to initiate motion of sediment given constant bed shear stress and local velocity. If
all things remain equal otherwise, then this should decrease the area of enhanced
deposition because it's easier to entrain sediment. I would hypothesize that with
increasing grain size, the effect of turbulence on sediment deposition should
decrease.
Future research should be focused on verifying the stipulations discussed
above. For patches of vegetation with a predicted steady wake region, is there an
enhanced sediment deposition? In addition, if there is enhanced sediment
deposition in the steady wake region, does it correspond to the stipulated low
values of mean velocity and turbulence? For the flexible vegetation, it would be
75
interesting to investigate if there are ever cases that experience enhanced
deposition. If the upstream velocity is increased, there may be a steady wake region
that develops downstream of the patch. If the size of the patch is increased, the wake
recovery length is delayed because the lateral and vertical turbulence structures
take longer to reach the centerline of the flume downstream of the patch because
the flow field scales on the patch size. It would be interesting to investigate the
deposition behind a rigid submerged patch rather than emergent behavior, which
would also have vertical turbulence structures similar to those seen in the flexible
submerged cases. It could even be possible to construct a flexible vegetation patch
where the canopy height is at the free surface equal to the water depth. All of these
cases could be investigate to see if the proposed argument for enhanced sediment
deposition remains valid.
76
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f
Appendix
The appendix contains 12 tables of the raw velocity and deposition data along the centerline of the flume for
each experiment including the control experiments.
Table 1. Rigid Control Case - Raw velocity data along centerline of flume with measured standard deviation.
Rigid Control
(cm)
-95
-95
-50
-50
0
0
30
50
80
130
200
280
300
300
300
300
400
Error
(cm)
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Urms
Ux
X Position
Value
Value
(cm/s)
8.9
9.3
9.4
9.3
9.4
9.3
9.4
9.4
9.6
9.6
9.5
9.8
9.6
9.3
8.9
9.0
9.4
Error
(cm/s)
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
Value
(cm/s)
1.4
1.4
1.5
1.3
1.6
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.4
1.4
1.8
1.7
1.3
Error
(cm/s)
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
Vrms
Value
(cm/s)
1.2
1.0
0.9
0.8
0.9
0.7
0.7
0.8
0.7
0.7
0.6
0.6
0.7
0.7
1.0
0.8
0.6
Wrms
Error
Value
Error
(cm/s)
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
(cm/s)
0.6
0.7
0.6
0.6
0.6
0.5
0.5
0.5
0.5
0.5
0.4
0.4
0.5
0.5
0.7
0.5
0.4
(cm/s)
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
81
WAVWNNMNW"
mw
--
x
Position
Value
-,
640
Ux
Error
(cm)
1
1
1
Urms
Value
(cm/s)
9.6
9.4
9.5
Vrms
Error
(cm/s)
0.1
0.1
0.1
Wrms
Value
(cm/s)
1.3
1.3
1.3
x
Position
Value
(cm)
0.3
0.3
0.3
Ux
Error
(cm)
0.6
0.6
0.7
Urms
Value
(cm/s)
0.3
0.3
0.3
700
1
9.5
0.1
1.4
0.3
0.7
770
1
9.4
0.1
1.5
0.3
0.7
(cm)
520
580
82
Vrms
Error
(cm/s)
0.4
0.5
0.5
Wrms
Value
(cm/s)
0.3
0.3
0.3
0.3
0.5
0.3
0.3
0.5
0.3
Table 2. Rigid Control - Raw deposition data along centerline of flume with measured standard deviation.
Rigid Control
Net Deposition
X Position
Error
Value
Error
Value
(cm)
-100
-50
-10
30
70
110
150
190
230
270
300
340
380
420
460
500
540
580
600
620
640
660
680
700
720
740
(cm)
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
(g/cm2)
0.0017
0.0025
0.0025
0.0026
0.0025
0.0025
0.0025
0.0025
0.0025
0.0025
0.0024
0.0025
0.0026
0.0026
0.0025
0.0025
0.0025
0.0025
0.0025
0.0025
0.0026
0.0025
0.0025
0.0025
0.0024
0.0024
(g/cm2)
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
83
84
Table 3. Case 1 - Raw velocity data along centerline of flume with measured standard deviation.
Rigid Dense - Case 1
X Position
Error
Value
(cm)
(cm)
-120
-100
-100
-80
-80
-60
-60
-50
-40
-40
-20
-20
-15
-10
-10
-5
-5
-2
-2
45
45
45
50
50
55
55
60
Ux
Value
(cm/s)
8.9
9.1
9.8
9.1
9.7
9.0
9.6
9.6
8.8
9.4
8.1
8.6
7.7
7.2
7.8
6.3
7.1
5.5
6.1
1.5
1.5
1.1
0.9
0.9
0.9
0.8
0.8
Error
(cm/s)
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
Urms
Error
Value
(cm/s)
(cm/s)
0.7
0.3
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.6
0.6
0.7
0.6
0.7
0.7
0.7
0.7
0.6
0.7
0.7
0.6
0.6
0.7
0.4
0.4
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
Vrms
Error
Value
(cm/s) (cm/s)
0.7
0.3
0.6
0.3
0.3
0.6
0.3
0.6
0.6
0.3
0.6
0.3
0.6
0.6
0.3
0.6
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.6
0.6
0.6
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.4
0.3
0.3
0.3
85
0.3
Wrms
Error
Value
(cm/s) (cm/s)
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.3
0.4
0.3
0.4
0.3
0.3
0.3
0.2
0.2
0.2
0.2
0.2
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
mmwmow-
P-O
X Position
Error
Value
(cm)
(cm)
Ux
Value
(cm/s)
Error
(cm/s)
Urms
Value
Value
(cm)
(cm/s)
Vrms
Value
Error
(cm/s)
(cm)
Wrms
Value
Error
(cm/s) (cm/s)
60
65
70
70
80
80
1
1
1
1
1
1
0.9
0.7
0.7
0.8
0.5
0.6
0.1
0.1
0.1
0.1
0.1
0.1
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.2
0.2
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.2
0.1
0.2
0.2
0.2
0.2
0.3
0.3
0.3
0.3
0.3
0.3
90
100
100
100
110
110
120
130
140
140
150
1
1
1
1
1
1
1
1
1
1
1
0.6
0.4
0.4
0.3
0.3
0.4
0.1
-0.6
-0.7
-0.9
-0.5
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.3
0.3
0.3
0.5
0.3
0.4
0.5
1.2
1.3
1.3
1.5
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.4
0.4
0.7
0.8
0.9
0.7
1.4
2.7
2.7
2.6
2.9
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.1
0.1
0.1
0.2
0.1
0.2
0.2
0.7
0.8
0.8
0.8
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
160
1
-0.2
0.1
2.0
0.3
3.5
0.3
0.9
0.3
160
170
180
1
1
1
0.2
0.9
2.8
0.1
0.1
0.1
2.0
2.5
2.8
0.3
0.3
0.3
3.7
4.0
4.4
0.3
0.3
0.3
0.9
0.9
0.9
0.3
0.3
0.3
190
200
1
1
2.0
2.5
0.1
0.1
2.5
2.6
0.3
0.3
3.9
3.8
0.3
0.3
0.9
0.9
0.3
0.3
200
1
5.0
0.1
3.0
0.3
4.6
0.3
1.0
0.3
200
1
4.9
0.1
2.5
0.3
4.7
0.3
1.0
0.3
210
1
5.3
0.1
2.4
0.3
4.7
0.3
1.0
0.3
220
1
3.5
0.1
3.0
0.3
3.9
0.3
0.9
0.3
230
240
1
1
6.8
6.0
0.1
0.1
2.8
2.6
0.3
0.3
4.4
4.1
0.3
0.3
1.0
0.9
0.3
0.3
86
X Position
Value
Error
(cm)
(cm)
250
1
260
1
280
1
Ux
Value
(cm/s)
7.4
7.5
8.2
Error
(cm/s)
0.1
0.1
0.1
Urms
Value
Value
(cm)
(cm/s)
2.0
0.3
2.1
0.3
2.0
0.3
Vrms
Error
Value
(cm)
(cm/s)
4.0
0.3
3.9
0.3
3.7
0.3
Wrms
Error
Value
(cm/s) (cm/s)
0.9
0.3
0.9
0.3
0.9
0.3
300
300
320
340
360
1
1
1
1
1
8.5
8.0
8.1
9.4
9.2
0.1
0.1
0.1
0.1
0.1
1.9
1.8
1.9
1.6
1.7
0.3
0.3
0.3
0.3
0.3
3.5
3.3
3.1
3.0
2.8
0.3
0.3
0.3
0.3
0.3
0.9
0.9
0.9
0.9
0.8
0.3
0.3
0.3
0.3
0.3
380
1
10.0
0.1
1.7
0.3
2.9
0.3
0.8
0.3
380
400
420
1
1
1
8.8
8.6
10.0
0.1
0.1
0.1
1.7
2.0
1.7
0.3
0.3
0.3
2.7
2.7
2.5
0.3
0.3
0.3
0.8
0.8
0.8
0.3
0.3
0.3
420
450
460
500
500
550
1
1
1
1
1
1
9.7
10.5
10.2
11.1
10.6
10.7
0.1
0.1
0.1
0.1
0.1
0.1
1.5
1.7
1.5
1.6
1.7
1.5
0.3
0.3
0.3
0.3
0.3
0.3
2.5
2.5
2.3
2.1
2.1
1.9
0.3
0.3
0.3
0.3
0.3
0.3
0.8
0.8
0.8
0.8
0.8
0.7
0.3
0.3
0.3
0.3
0.3
0.3
600
1
10.5
0.1
1.3
0.3
1.6
0.3
0.7
0.3
87
Table 4. Case 1 - Raw deposition data along centerline of flume for each replicate with measured standard deviation and the mean of
the replicates.
Net Deposition
X Position
Replicate 1
Value Error Value
Error
(cm)
(cm)
(g/cm2) (g/cm2)
-100
-90
-80
-70
-60
-50
-40
-30
0.0021
0.0029
0.0031
0.0032
0.0020
0.0032
0.0032
0.0032
-20
0.0032
-10
0
0.0031
0.0026
0.0029
42
43
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
Rigid Dense - Case 1
Net Deposition
Net Deposition
Replicate 2
Value
Error
(g/cm2) (g/cm2)
0.0024
0.0036
0.0037
0.0040
0.0026
0.0039
0.0037
0.0038
0.0037
0.0032
0.0024
0.0028
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
Replicate 3
Value
Error
(g/cm2) (g/cm2)
0.0010
0.0019
0.0021
0.0023
0.0022
0.0025
0.0024
0.0025
Mean Net
Deposition
Value
Error
(g/cm2) (g/cm2)
0.0018
0.0028
0.0030
0.0032
0.0022
0.0032
0.0031
0.0032
0.0007
0.0008
0.0008
0.0009
0.0003
0.0007
0.0006
0.0007
0.0032
0.0006
0.0030
0.0025
0.0026
0.0024
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0029
0.0003
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0026
0.0034
0.0027
0.0032
0.0031
0.0030
0.0031
0.0030
0.0028
0.0002
0.0005
0.0001
0.0001
0.0001
0.0002
0.0002
0.0003
0.0026
50
60
70
80
90
100
110
120
0.0036
0.0032
0.0033
0.0032
0.0031
0.0032
0.0030
0.0030
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0033
0.0029
0.0030
0.0031
0.0030
0.0032
0.0031
0.0029
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0026
0.0032
0.0021
0.0033
0.0031
0.0030
0.0029
0.0028
0.0024
130
0.0028
0.0001
0.0027
0.0001
0.0026
0.0001
0.0027
0.0001
140
150
0.0026
0.0024
0.0001
0.0001
0.0025
0.0022
0.0001
0.0001
0.0022
0.0021
0.0001
0.0001
0.0024
0.0022
0.0002
0.0002
88
Net Deposition
Replicate 1
X Position
Error
Value Error Value
(cm)
(cm)
(g/cm2) (g/cm2)
160
170
180
190
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340
350
360
370
380
390
400
410
420
430
0.0022
0.0021
0.0023
0.0023
0.0023
0.0021
0.0020
0.0019
0.0020
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
Net Deposition
Replicate 2
Error
Value
(g/cm2) (g/cm2)
0.0022
0.0019
0.0020
0.0020
0.0020
0.0021
0.0019
0.0016
0.0019
0.0019
0.0020
0.0019
0.0020
0.0019
0.0019
0.0020
0.0017
0.0015
0.0019
0.0019
0.0001
0.0016
0.0016
0.00 14
0.00 15
0.0015
0.0015
0.0013
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0017
0.0016
0.0018
0.0015
0.0017
0.0016
0.0015
0.0016
0.0015
0.0016
0.0015
0.0013
0.0016
0.0015
0.0016
0.0015
0.0013
0.0015
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
Net Deposition
Replicate 3
Error
Value
(g/cm2) (g/cm2)
0.0020
0.0020
0.0021
0.0021
0.0020
0.0020
0.0021
0.0020
0.0021
0.0019
0.0020
0.0020
0.0021
0.0021
0.0021
0.0021
0.0021
0.0021
0.0020
0.0019
0.0021
0.0021
0.0022
0.0021
0.0021
0.0020
0.0021
0.0018
89
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
Mean Net
Deposition
Error
Value
(g/cm2) (g/cm2)
0.0021
0.0020
0.0021
0.0021
0.0021
0.0021
0.0020
0.0018
0.0020
0.0019
0.0019
0.0019
0.0019
0.0018
0.0019
0.0019
0.0018
0.0017
0.0018
0.0018
0.0018
0.0016
0.0018
0.0017
0.0018
0.0016
0.0016
0.0015
0.0001
0.0001
0.0001
0.0002
0.0002
0.0001
0.0001
0.0002
0.0001
0.0000
0.0002
0.0002
0.0002
0.0003
0.0002
0.0003
0.0003
0.0003
0.0003
0.0002
0.0005
0.0004
0.0003
0.0004
0.0003
0.0003
0.0004
0.0002
-,
. -1........
Q..*
-
---
X Position
Value Error
(cm)
(cm)
440
450
460
470
480
490
500
510
520
530
540
550
560
570
580
590
600
610
620
630
640
650
660
670
680
690
700
710
720
Net Deposition
Replicate 1
Value
Error
(g/cm2) (g/cm2)
0.0015
0.0001
0.0016
0.0001
0.0014
0.0001
0.0016
0.0001
0.0016
0.0001
0.0017
0.0001
0.0017
0.0001
0.0001
0.0019
0.0018
0.0001
0.0016
0.0001
0.0018
0.0001
0.0019
0.0001
0.0020
0.0001
0.0019
0.0001
0.0017
0.0001
0.0019
0.0001
0.0017
0.0001
Net Deposition
Replicate 2
Value
Error
(g/cm2) (g/cm2)
0.0012
0.0001
0.0013
0.0001
0.0011
0.0001
0.0015
0.0001
0.0015
0.0001
0.0014
0.0001
0.0013
0.0001
0.0014
0.0001
0.0013
0.0001
0.0014
0.0001
0.0013
0.0001
0.0013
0.0001
0.0015
0.0001
0.0013
0.0001
0.0012
0.0001
0.0014
0.0001
0.0014
0.0001
Net Deposition
Replicate 3
Value
Error
(g/cm2) (g/cm2)
0.0020
0.0001
0.0019
0.0001
0.0020
0.0001
0.0020
0.0001
0.0019
0.0001
0.0019
0.0001
0.0018
0.0001
0.0020
0.0001
0.0020
0.0001
0.0020
0.0001
0.0020
0.0001
0.0020
0.0001
0.0019
0.0001
0.0019
0.0001
0.0019
0.0001
0.0019
0.0001
0.0020
0.0001
0.0020
0.0001
0.0019
0.0001
0.0019
0.0001
0.0019
0.0001
0.0020
0.0001
0.0019
0.0001
0.0019
0.0001
0.0019
0.0001
0.0020
0.0001
0.0020
0.0001
0.0020
0.0001
0.0019
0.0001
90
Mean Net
Deposition
Value
Error
(g/cm2) (g/cm2)
0.0016
0.0004
0.0016
0.0003
0.0015
0.0004
0.0017
0.0002
0.0017
0.0002
0.0017
0.0003
0.0016
0.0002
0.0018
0.0003
0.0017
0.0003
0.0017
0.0003
0.0017
0.0003
0.0017
0.0004
0.0018
0.0003
0.0017
0.0016
0.0017
0.0017
0.0020
0.0019
0.0019
0.0019
0.0020
0.0019
0.0019
0.0019
0.0020
0.0020
0.0020
0.0019
0.0003
0.0003
0.0003
0.0003
X Position
Value Error
(cm)
(cm)
Net Deposition
Replicate 1
Error
Value
(g/cm2) (g/cm2)
Net Deposition
Replicate 2
Error
Value
(g/cm2) (g/cm2)
Net Deposition
Replicate 3
Error
Value
(g/cm2) (g/cm2)
Mean Net
Deposition
Error
Value
(g/cm2) (g/cm2)
730
740
750
760
770
780
790
800
810
3
3
3
3
3
3
3
3
3
-
-
-
-
0.0020
0.0020
0.0021
0.0020
0.0020
0.0020
0.0020
0.0021
0.0020
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0020
0.0020
0.0021
0.0020
0.0020
0.0020
0.0020
0.0021
0.0020
-
820
3
-
-
-
-
0.0019
0.0001
0.0019
-
830
840
850
860
870
3
3
3
3
3
-
-
-
-
-
-
0.0020
0.0020
0.0020
0.0020
0.0020
0.0001
0.0001
0.0001
0.0001
0.0001
0.0020
0.0020
0.0020
0.0020
0.0020
-
91
Table 5. Case 2 - Raw velocity data along centerline of flume with measured standard deviation.
Rigid Sparse - Case 2
X Position
Error
Value
(cm)
(cm)
-200
-180
-100
-70
-50
-30
-10
-5
-2
-1
2.5
6
16
23
33
40
44
45
45
45
50
50
60
70
70
80
84
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Ux
Value
(cm/s)
Error
(cm/s)
Value
cms
9.16
9.69
9.61
9.57
9.42
9.20
8.70
8.28
7.85
8.26
8.13
8.32
7.47
7.42
6.97
6.10
5.62
6.14
5.48
5.96
4.92
5.59
5.22
4.39
5.08
5.08
5.05
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.9
0.9
0.9
1.0
1.0
1.0
1.2
1.1
1.0
1.0
1.8
1.8
2.7
2.3
1.7
1.8
1.4
1.4
1.3
1.4
0.9
1.0
0.8
0.5
0.6
0.7
0.4
Urms
Error
cm/s)
Vrms
Error
Value
(cm/s)
(cm/s)
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
1.4
1.7
2.4
2.1
1.6
1.8
1.3
1.2
1.2
1.2
0.9
0.8
0.6
0.5
0.4
0.4
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
92
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
Wrms
Error
Value
(cm/s)
(cm/s)
0.4
0.4
0.4
0.4
0.4
0.4
0.5
0.5
0.5
0.5
0.7
0.7
0.8
0.8
0.7
0.7
0.6
0.6
0.6
0.6
0.4
0.5
0.3
0.2
0.3
0.3
0.2
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
X Position
Value
Error
(cm)
90
100
100
120
120
140
150
160
200
200
200
240
250
280
300
300
320
350
360
400
400
400
450
450
500
500
500
550
550
(cm)
Ux
Value
Error
(cm/s)
4.43
4.80
4.99
4.60
5.06
4.99
4.34
4.89
4.41
4.91
4.92
4.83
4.46
4.88
4.73
5.04
5.03
4.97
5.48
5.94
5.47
5.74
6.22
6.37
6.59
6.72
6.43
6.56
7.39
(cm/s)
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
Value
j
Urms
Value
(cm/s)
0.4
0.4
0.4
0.3
0.6
0.5
0.4
0.5
0.5
0.4
0.5
0.6
0.5
0.6
0.6
0.5
0.7
0.9
1.0
1.3
0.7
1.0
1.2
1.3
1.2
1.3
1.2
1.2
1.4
Error
(cm)
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
93
Vrms
Value
Wrms
Error
Value
(cm)
0.3
0.3
0.3
0.4
0.3
0.3
0.3
0.3
0.5
0.4
(cm/s)
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
(cm/s)
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.1
0.4
0.3
0.2
0.5
0.8
0.6
1.0
0.6
0.8
1.2
1.2
1.5
1.0
1.2
1.3
1.3
1.2
1.3
1.2
1.2
1.1
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.2
0.2
0.2
0.4
0.2
0.4
0.5
0.5
0.6
0.4
0.5
0.6
0.5
0.5
0.6
0.5
0.5
0.6
0.3
(cm/s)
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
X Position
Ux
Urms
Vrms
Wrms
Value
(cm)
Error
(cm)
Value
(cm/s)
Error
(cm/s)
Value
(cm/s)
Value
(cm)
Error
(cm)
Value
(cm/s)
Error
(cm/s)
Value
(cm/s)
600
600
650
700
750
800
850
900
1
1
1
1
1
1
1
1
7.49
7.44
7.75
8.57
8.93
8.98
9.13
9.08
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
1.2
1.3
1.2
1.2
1.2
1.0
1.2
1.1
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
1.3
1.2
1.2
1.2
1.1
1.0
0.9
0.8
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.6
0.6
0.5
0.5
0.5
0.5
0.5
0.5
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
94
Table 6. Case 2 - Raw deposition data along centerline of flume for each replicate with measured standard deviation and the mean of
the replicates.
X Position
Value
Error
(cm)
(cm)
-100
3
-90
3
-80
3
-70
3
-60
3
-50
3
-40
3
-30
3
-20
3
-10
3
0
3
5
3
3
11
18
3
3
22
28
3
35
3
42
3
43
3
50
3
60
3
70
3
80
3
90
3
100
3
Net Deposition
Replicate 1
Value
Error
(g/cm2)
(g/cm2)
0.0021
0.0001
0.0024
0.0001
0.0022
0.0001
0.0022
0.0001
0.0014
0.0001
0.0020
0.0001
0.0024
0.0001
0.0024
0.0001
0.0025
0.0001
0.0026
0.0001
0.0015
0.0001
0.0022
0.0001
0.0025
0.0001
0.0025
0.0001
0.0026
0.0001
0.0027
0.0001
0.0027
0.0001
0.0029
0.0001
Rigid Sparse - Case 2
Net Deposition
Net Deposition
Replicate 2
Replicate 3
Value
Error
Value
Error
(g/cm2)
(g/cm2)
(g/cm2)
(g/cm2)
0.0028
0.0001
0.0012
0.0001
0.0028
0.0001
0.0020
0.0001
0.0026
0.0001
0.0026
0.0001
0.0023
0.0001
0.0022
0.0001
0.0020
0.0001
0.0027
0.0001
0.0022
0.0001
0.0031
0.0001
0.0024
0.0001
0.0029
0.0001
0.0025
0.0029
0.0001
0.0001
0.0025
0.0001
0.0029
0.0001
0.0026
0.0001
0.0029
0.0001
0.0017
0.0001
0.0028
0.0001
0.0018
0.0001
0.0001
0.0017
0.0016
0.0001
0.0018
0.0001
0.0016
0.0001
0.0001
0.0018
0.0025
0.0001
0.0020
0.0001
0.0027
0.0001
0.0020
0.0001
0.0027
0.0001
0.0025
0.0001
0.0029
0.0001
0.0025
0.0001
0.0029
0.0001
0.0026
0.0001
0.0030
0.0001
0.0027
0.0001
0.0031
0.0001
0.0029
0.0001
95
Mean Net
Deposition
Value
Error
(g/cm2)
(g/cm2)
0.0020
0.0008
0.0024
0.0004
0.0025
0.0002
0.0023
0.0000
0.0020
0.0006
0.0024
0.0006
0.0026
0.0003
0.0026
0.0003
0.0027
0.0002
0.0027
0.0002
0.0020
0.0007
0.0018
0.0017
0.0016
0.0018
0.0016
0.0018
0.0023
0.0002
0.0020
0.0024
0.0004
0.0025
0.0001
0.0027
0.0002
0.0027
0.0002
0.0028
0.0001
0.0030
0.0001
X Position
Value
Error
(cm)
(cm)
110
3
120
3
130
3
140
3
150
3
160
3
170
3
180
3
190
3
200
3
210
3
220
3
230
3
240
3
250
3
260
3
270
3
280
3
290
3
300
3
310
3
320
3
330
3
340
3
350
3
360
3
370
3
380
3
390
3
Net Deposition
Replicate 1
Value
Error
(g/cm2)
(g/cm2)
0.0029
0.0001
0.0029
0.0001
0.0029
0.0001
0.0029
0.0001
0.0029
0.0001
0.0030
0.0001
0.0031
0.0001
0.0031
0.0001
0.0031
0.0001
0.0030
0.0001
0.0030
0.0001
0.0030
0.0001
0.0029
0.0001
0.0029
0.0001
0.0028
0.0001
0.0028
0.0001
0.0029
0.0001
0.0028
0.0001
0.0028
0.0001
0.0028
0.0001
0.0027
0.0001
0.0028
0.0001
0.0027
0.0001
0.0028
0.0001
0.0026
0.0001
0.0025
0.0001
0.0024
0.0001
0.0024
0.0001
0.0025
0.0001
Net Deposition
Replicate 2
Value
Value
(g/cm2)
(cm)
0.0031
0.0001
0.0030
0.0001
0.0032
0.0001
0.0032
0.0001
0.0033
0.0001
0.0033
0.0001
0.0033
0.0001
0.0033
0.0001
0.0033
0.0001
0.0033
0.0001
0.0034
0.0001
0.0033
0.0001
0.0032
0.0001
0.0032
0.0001
0.0031
0.0001
0.0031
0.0001
0.0032
0.0001
0.0032
0.0001
0.0032
0.0001
0.0031
0.0001
0.0031
0.0001
0.0030
0.0001
0.0030
0.0001
0.0031
0.0001
0.0029
0.0001
0.0028
0.0001
0.0028
0.0001
0.0027
0.0001
0.0028
0.0001
Net Deposition
Replicate 3
Error
Value
(cm)
(g/cm2)
0.0029
0.0001
0.0032
0.0001
0.0031
0.0001
0.0030
0.0001
0.0030
0.0001
0.0030
0.0001
0.0031
0.0001
0.0033
0.0001
0.0032
0.0001
0.0031
0.0001
0.0030
0.0001
0.0029
0.0001
0.0030
0.0001
0.0030
0.0001
0.0029
0.0001
0.0029
0.0001
0.0029
0.0001
0.0028
0.0001
0.0027
0.0001
0.0028
0.0001
0.0027
0.0001
0.0027
0.0001
0.0027
0.0001
0.0026
0.0001
0.0026
0.0001
0.0026
0.0001
0.0026
0.0001
0.0024
0.0001
0.0024
0.0001
96
Mean Net
Deposition
Error
Value
(g/cm2)
(g/cm2)
0.0030
0.0001
0.0030
0.0001
0.0031
0.0002
0.0031
0.0002
0.0031
0.0002
0.0031
0.0002
0.0031
0.0001
0.0032
0.0001
0.0001
0.0032
0.0031
0.0002
0.0031
0.0002
0.0031
0.0002
0.0030
0.0002
0.0030
0.0001
0.0029
0.0002
0.0029
0.0002
0.0030
0.0002
0.0030
0.0002
0.0029
0.0002
0.0029
0.0001
0.0028
0.0002
0.0028
0.0002
0.0028
0.0002
0.0028
0.0002
0.0027
0.0002
0.0026
0.0002
0.0026
0.0002
0.0025
0.0002
0.0026
0.0002
X Position
Value
Error
(cm)
(cm)
400
410
420
430
440
450
460
470
480
490
500
510
520
530
540
550
560
570
580
590
600
610
620
630
640
650
660
670
680
Net Deposition
Replicate 1
Value
Error
(g/cm2)
(g/cm2)
0.0025
0.0001
0.0025
0.0001
0.0025
0.0001
0.0024
0.0001
0.0024
0.0001
0.0024
0.0001
0.0023
0.0001
0.0024
0.0001
0.0024
0.0001
0.0024
0.0001
0.0024
0.0001
0.0024
0.0001
0.0023
0.0001
0.0022
0.0001
0.0022
0.0001
0.0001
0.0022
Net Deposition
Replicate 2
Value
Value
(g/cm2)
(cm)
0.0028
0.0001
0.0001
0.0028
0.0028
0.0001
0.0028
0.0001
0.0026
0.0001
0.0026
0.0001
0.0026
0.0001
0.0026
0.0001
0.0026
0.0001
0.0026
0.0001
0.0026
0.0001
0.0001
0.0025
0.0025
0.0001
0.0025
0.0001
0.0025
0.0001
0.0025
0.0001
Net Deposition
Replicate 3
Value
Error
(cm)
(g/cm2)
0.0001
0.0024
0.0001
0.0023
0.0001
0.0024
0.0001
0.0024
0.0001
0.0023
0.0001
0.0023
0.0001
0.0024
0.0001
0.0023
0.0024
0.0001
0.0001
0.0024
0.0024
0.0001
0.0001
0.0024
0.0001
0.0023
0.0023
0.0001
0.0023
0.0001
0.0023
0.0001
0.0023
0.0001
0.0023
0.0001
0.0022
0.0001
0.0022
0.0001
0.0001
0.0023
0.0001
0.0023
0.0001
0.0022
0.0001
0.0022
0.0001
0.0022
0.0023
0.0001
0.0023
0.0001
0.0023
0.0001
0.0023
0.0001
97
Mean Net
Deposition
Error
Value
(g/cm2)
(g/cm2)
0.0026
0.0002
0.0025
0.0002
0.0025
0.0002
0.0025
0.0002
0.0024
0.0002
0.0025
0.0002
0.0024
0.0002
0.0024
0.0001
0.0024
0.0001
0.0025
0.0001
0.0025
0.0001
0.0024
0.0001
0.0023
0.0001
0.0023
0.0002
0.0023
0.0001
0.0023
0.0002
0.0023
0.0023
0.0022
0.0022
0.0023
0.0023
0.0022
0.0022
0.0022
0.0023
0.0023
0.0023
0.0023
X Position
Value
Error
(cm)
(cm)
690
3
700
3
710
3
720
3
730
3
740
3
750
3
760
3
770
3
780
3
790
3
800
3
Net Deposition
Replicate 1
Value
Error
(g/cm2)
(g/cm2)
-
Net Deposition
Replicate 2
Value
Value
(g/cm2)
(cm)
-
Net Deposition
Replicate 3
Error
Value
(cm)
(g/cm2)
0.0023
0.0001
0.0023
0.0001
0.0022
0.0001
0.0022
0.0001
0.0023
0.0001
0.0023
0.0001
0.0023
0.0001
0.0023
0.0001
0.0023
0.0001
0.0022
0.0001
0.0023
0.0001
0.0023
0.0001
Mean Net
Deposition
Error
Value
(g/cm2)
(g/cm2)
0.0023
0.0023
0.0022
0.0022
0.0023
0.0023
0.0023
0.0023
0.0023
0.0022
0.0023
0.0023
-
810
3
-
-
-
-
0.0022
0.0001
0.0022
-
820
830
3
3
-
-
-
-
-
-
0.0022
0.0022
0.0001
0.0001
0.0022
0.0022
-
98
Table 7. Flexible Control - Raw velocity data along centerline of flume with measured standard deviation.
Flexible Control
Z Position
X Position
Value Error Value Error
(cm)
(cm)
(cm)
(cm)
-95
-95
-95
-50
-50
-50
-50
-50
-50
0
0
0
10
30
30
50
50
50
80
80
80
130
130
130
200
15.0
10.0
6.0
15.0
15.0
10.0
10.0
6.0
6.0
15.0
10.0
6.0
6.0
15.0
10.0
15.0
10.0
6.0
15.0
10.0
6.0
15.0
10.0
6.0
15.0
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
Ux
Value
(cm/s)
Error
(cm/s)
7.8
7.7
7.1
8.2
8.1
7.6
7.9
7.4
7.2
8.2
7.2
7.3
8.0
8.2
7.4
8.1
7.9
8.0
7.9
7.7
8.2
7.8
7.7
8.3
8.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
Urms
Error
Value
(cm/s) (cm/s)
1.5
1.4
1.5
1.4
1.3
1.5
1.4
1.5
1.6
1.3
1.5
1.3
1.4
1.4
1.5
1.4
1.3
1.3
1.6
1.3
1.2
1.6
1.3
1.2
1.5
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
99
Vrms
Error
Value
(cm/s) (cm/s)
1.3
1.2
1.3
1.1
1.0
1.2
1.2
1.1
1.3
1.0
1.1
1.0
1.1
1.0
1.1
1.0
1.0
1.0
0.9
0.9
0.9
0.9
0.9
0.8
0.8
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
Wrms
Error
Value
(cm/s)
(cm/s)
0.8
0.8
0.7
0.7
0.7
0.7
0.8
0.7
0.7
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.5
0.6
0.5
0.5
0.5
0.5
0.5
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
X Position
Z Position
Value Error Value Error
Ux
Value
Error
Urms
Value
Error
Vrms
Value
Error
Wrms
Value
Error
(cm)
(cm)
(cm)
(cm)
(cm/s)
(cm/s)
(cm)
(cm)
(cm)
(cm)
(cm/s)
(cm/s)
200
200
280
280
280
300
300
300
300
300
300
300
300
1
1
1
1
1
1
1
1
1
1
1
1
1
10.0
6.0
15.0
10.0
6.0
15.0
15.0
14.0
13.0
12.0
11.0
10.0
9.0
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
7.1
8.6
8.1
8.4
7.9
8.4
8.0
8.3
8.0
8.0
8.1
8.1
8.2
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
1.5
1.1
1.4
1.2
1.2
1.1
1.1
1.1
1.1
1.3
1.7
1.4
1.2
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.9
0.7
0.8
0.7
0.7
0.6
0.7
0.7
0.7
0.9
1.7
1.1
1.1
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.5
0.5
0.4
0.5
0.4
0.4
0.4
0.4
0.4
0.5
0.5
0.5
0.5
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
300
1
8.0
0.5
8.5
0.1
1.1
0.3
0.7
0.3
0.4
0.3
300
300
300
300
300
300
300
300
300
300
400
400
400
520
520
520
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
7.0
6.0
6.0
5.0
4.0
3.0
2.0
1.0
0.0
-1.0
15.0
10.0
6.0
15.0
10.0
6.0
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
8.3
8.0
8.3
7.8
7.6
7.1
6.9
6.8
5.8
0.0
8.1
8.6
8.1
8.2
7.8
7.8
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
1.1
1.1
1.1
1.1
1.1
1.2
1.1
1.2
1.1
0.1
1.5
1.5
1.1
1.5
1.6
1.2
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.7
0.7
0.7
0.7
0.8
0.8
0.8
0.9
0.9
0.0
0.8
1.0
0.7
0.8
1.1
0.7
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.3
0.0
0.4
0.5
0.4
0.4
0.5
0.4
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.5
0.5
0.5
0.5
100
Ux
Z Position
X Position
Error
Value Error Value Error Value
(cm/s) (cm/s)
(cm)
(cm)
(cm)
(cm)
580
580
580
640
640
640
640
700
700
700
700
770
770
770
1
1
1
1
1
1
1
1
1
1
1
1
1
1
15.0
10.0
6.0
15.0
10.0
6.0
6.0
15.0
10.0
6.0
6.0
15.0
10.0
6.0
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
8.0
7.8
7.8
7.8
8.2
7.8
8.2
8.0
8.2
8.2
7.9
7.9
8.0
8.0
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
Urms
Error
Value
(cm)
(cm)
1.6
1.3
1.1
1.7
1.4
1.4
1.0
1.6
1.5
1.5
1.5
1.6
1.6
1.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
101
Vrms
Error
Value
(cm)
(cm)
0.9
0.6
0.7
0.9
0.8
0.8
0.6
0.7
0.9
0.8
0.8
0.8
0.9
0.8
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
Wrms
Error
Value
(cm/s) (cm/s)
0.4
0.4
0.4
0.4
0.4
0.5
0.4
0.4
0.5
0.5
0.5
0.4
0.5
0.5
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
Table 8. Flexible Control - Raw deposition data along centerline of flume with measured standard deviation.
Flexible Control
X Position
Net Deposition
Value Error Value
Error
(cm) (cm)
(g/cm2) (g/cm2)
-100
1
0.0021
0.0001
-50
1
0.0024
0.0001
-10
1
0.0024
0.0001
30
1
0.0027
0.0001
70
1
0.0027
0.0001
110
1
0.0027
0.0001
150
1
0.0026
0.0001
190
1
0.0026
0.0001
230
1
0.0027
0.0001
270
1
0.0027
0.0001
300
1
0.0028
0.0001
340
1
0.0026
0.0001
380
1
0.0026
0.0001
420
1
0.0028
0.0001
460
1
0.0027
0.0001
500
1
0.0025
0.0001
540
1
0.0026
0.0001
580
1
0.0026
0.0001
600
1
0.0026
0.0001
620
1
0.0026
0.0001
640
1
0.0027
0.0001
660
1
0.0027
0.0001
680
1
0.0026
0.0001
700
1
0.0025
0.0001
720
1
0.0026
0.0001
102
X Position
Value Error
(cm)
(cm)
740
1
760
1
780
1
800
1
820
1
830
1
840
1
Net Deposition
Value
Error
(cm)
(cm)
0.0026
0.0001
0.0025
0.0001
0.0026
0.0001
0.0026
0.0001
0.0023
0.0001
0.0025
0.0001
0.0024
0.0001
103
Table 9. Case 3.- Raw velocity data along centerline with measured standard deviation.
X Position
Value Error
Z Position
Value Error
Flexible Dense - Case 3
Ux
Urms
Value
Error
Value
Error
Vrms
Value
Error
Wrms
Value
Error
(cm)
(cm)
(cm)
(cm)
(cm/s)
(cm/s)
(cm/s)
(cm/s)
(cm/s)
(cm/s)
(cm/s)
(cm/s)
-95
-95
-95
-50
-50
-50
-50
-50
-50
0
0
0
0
0
10
10
10
22
22
22
30
30
30
50
50
50
50
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
15.0
10.0
6.0
15.0
15.0
10.0
10.0
6.0
6.0
15.0
15.0
10.0
10.0
6.0
15.0
10.0
6.0
15.0
10.0
6.0
15.0
10.0
6.0
15.0
15.0
10.0
10.0
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
7.3
7.2
7.6
7.5
7.2
7.0
8.0
7.1
7.1
7.3
7.4
6.7
7.6
6.2
7.8
5.7
0.3
9.3
7.7
4.7
9.0
7.1
0.1
9.4
10.7
4.6
6.3
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
1.5
1.6
1.4
1.4
1.6
1.6
1.3
1.5
1.4
1.3
1.4
1.5
1.5
1.1
1.4
2.9
0.5
1.8
2.3
1.3
1.5
1.8
0.2
1.5
1.8
2.3
2.7
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
1.2
1.3
1.4
1.0
1.2
1.1
1.1
1.2
1.2
1.0
0.9
1.1
1.2
1.0
1.0
1.3
0.4
1.3
1.6
0.9
1.0
1.1
0.2
0.9
1.4
1.6
1.8
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.8
0.8
0.7
0.7
0.7
0.7
0.7
0.6
0.6
0.6
0.6
0.6
0.7
0.5
0.6
0.6
0.1
0.6
0.6
0.4
0.6
0.5
0.1
0.6
0.6
0.8
0.8
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
104
X Position
Value Error
(cm)
(cm)
50
50
80
80
80
100
100
100
130
130
130
200
200
200
200
200
200
280
280
280
400
400
400
400
400
400
520
520
520
580
Z Position
Value Error
(cm)
(cm)
6.0
6.0
15.0
10.0
6.0
15.0
10.0
6.0
15.0
10.0
6.0
15.0
15.0
10.0
10.0
6.0
6.0
15.0
10.0
6.0
15.0
15.0
10.0
10.0
6.0
6.0
15.0
10.0
6.0
15.0
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5,
0.5
0.5
0.5
Ux
Value
(cm/s)
Error
(cm/s)
-0.2
0.0
7.9
3.5
-0.5
7.8
3.2
1.3
5.6
5.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
2.9
5.8
3.1
5.5
3.7
4.8
5.7
6.2
7.0
5.9
6.7
7.3
7.1
6.7
6.4
6.2
7.1
7.5
6.9
7.4
Urms
Error
Value
(cm)
(cm)
0.5
0.4
2.1
2.8
1.7
2.2
3.4
1.9
2.2
1.8
1.5
1.5
2.2
1.3
3.0
1.4
1.4
1.3
1.3
1.3
1.2
1.2
1.2
1.7
1.1
1.2
1.1
1.1
1.1
1.0
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
105
Vrms
Error
Value
(cm)
(cm)
0.4
0.3
1.5
2.7
1.8
1.5
2.4
2.1
1.8
2.0
1.9
1.3
1.2
1.6
1.4
1.4
1.2
0.9
1.1
1.1
0.8
0.8
1.0
0.9
0.9
0.8
0.7
1.0
0.9
0.7
Wrms
Error
Value
(cm/s) (cm/s)
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.2
0.2
0.8
1.0
1.0
0.8
0.9
1.0
0.9
0.9
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.9
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.7
0.8
0.7
0.8
0.8
0.7
0.6
0.7
0.6
0.5
0.5
0.6
0.6
0.5
0.5
0.4
0.5
0.5
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.4
X Position
Value Error
(cm)
(cm)
1
580
1
580
1
640
1
640
1
640
1
700
1
700
700
1
770
1
770
1
1
770
Z Position
Value Error
(cm)
(cm)
0.5
10.0
0.5
6.0
0.5
15.0
0.5
10.0
0.5
6.0
0.5
15.0
0.5
10.0
0.5
6.0
15.0
0.5
10.0
0.5
0.5
6.0
Ux
Value
(cm/s)
7.3
7.0
7.5
7.5
7.0
7.4
7.6
7.0
7.5
7.3
7.0
Error
(cm/s)
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
Urms
Error
Value
(cm)
(cm)
0.3
1.0
0.3
1.1
0.3
1.0
0.3
1.0
0.3
1.1
0.3
1.0
0.3
1.3
0.3
1.0
0.3
1.0
0.3
1.7
0.3
1.0
106
Vrms
Error
Value
(cm)
(cm)
0.3
0.8
0.3
0.8
0.3
0.6
0.3
0.7
0.3
0.8
0.3
0.6
0.3
0.7
0.8
0.3
0.3
0.6
0.8
0.3
0.7
0.3
Wrms
Error
Value
(cm/s) (cm/s)
0.3
0.4
0.3
0.5
0.3
0.4
0.3
0.4
0.3
0.4
0.3
0.4
0.3
0.4
0.3
0.4
0.4
0.3
0.3
0.5
0.3
0.4
Table 10. Case 3 - Raw deposition data along centerline for each replicate with measured standard deviation and the mean of the
replicates.
Flexible Dense - Case 3
X Position
Value Error
(cm)
(cm)
-95
-95
-95
-50
-50
-50
-50
-50
-50
0
0
0
0
0
10
10
10
22
22
22
30
30
30
50
50
50
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Z Position
Error
Value
(cm)
(cm)
15.0
10.0
6.0
15.0
15.0
10.0
10.0
6.0
6.0
15.0
15.0
10.0
10.0
6.0
15.0
10.0
6.0
15.0
10.0
6.0
15.0
10.0
6.0
15.0
15.0
10.0
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
Ux
Value
(cm/s)
Error
(cm/s)
7.3
7.2
7.6
7.5
7.2
7.0
8.0
7.1
7.1
7.3
7.4
6.7
7.6
6.2
7.8
5.7
0.3
9.3
7.7
4.7
9.0
7.1
0.1
9.4
10.7
4.6
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
Urms
Error
Value
(cm/s) (cm/s)
1.5
1.6
1.4
1.4
1.6
1.6
1.3
1.5
1.4
1.3
1.4
1.5
1.5
1.1
1.4
2.9
0.5
1.8
2.3
1.3
1.5
1.8
0.2
1.5
1.8
2.3
107
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
Vrms
Error
Value
(cm/s) (cm/s)
1.2
1.3
1.4
1.0
1.2
1.1
1.1
1.2
1.2
1.0
0.9
1.1
1.2
1.0
1.0
1.3
0.4
1.3
1.6
0.9
1.0
1.1
0.2
0.9
1.4
1.6
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
Wrms
Error
Value
(cm/s) (cm/s)
0.8
0.8
0.7
0.7
0.7
0.7
0.7
0.6
0.6
0.6
0.6
0.6
0.7
0.5
0.6
0.6
0.1
0.6
0.6
0.4
0.6
0.5
0.1
0.6
0.6
0.8
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
X Position
Value Error
(cm)
50
50
50
80
80
80
100
100
100
130
130
130
200
200
200
200
200
200
280
280
280
400
400
400
400
400
400
520
520
(cm)
Z Position
Error
Value
Value
Error
Urms
Error
Value
Ux
Vrms
Error
Value
Wrms
Error
Value
(cm)
(cm)
(cm/s)
(cm/s)
(cm)
(cm)
(cm)
(cm)
(cm/s)
(cm/s)
10.0
6.0
6.0
15.0
10.0
6.0
15.0
10.0
6.0
15.0
10.0
6.0
15.0
15.0
10.0
10.0
6.0
6.0
15.0
10.0
6.0
15.0
15.0
10.0
10.0
6.0
6.0
15.0
10.0
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
6.3
-0.2
0.0
7.9
3.5
-0.5
7.8
3.2
1.3
5.6
5.1
2.9
5.8
3.1
5.5
3.7
4.8
5.7
6.2
7.0
5.9
6.7
7.3
7.1
6.7
6.4
6.2
7.1
7.5
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
2.7
0.5
0.4
2.1
2.8
1.7
2.2
3.4
1.9
2.2
1.8
1.5
1.5
2.2
1.3
3.0
1.4
1.4
1.3
1.3
1.3
1.2
1.2
1.2
1.7
1.1
1.2
1.1
1.1
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
1.8
0.4
0.3
1.5
0.8
0.2
0.2
0.8
1.0
1.0
0.8
0.9
1.0
0.9
0.9
0.9
0.7
0.8
0.7
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
1.0
0.3
0.5
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
108
0.3
0.3
0.3
0.3
0.3
0.3
0.3
2.7
1.8
1.5
2.4
2.1
1.8
2.0
1.9
1.3
1.2
1.6
1.4
1.4
1.2
0.9
1.1
1.1
0.8
0.8
1.0
0.9
0.9
0.8
0.7
0.8
0.8
0.7
0.6
0.7
0.6
0.5
0.5
0.6
0.6
0.5
0.5
0.4
X Position
Wrms
Vrms
Urms
Ux
Z Position
Value
(cm)
Error
(cm)
Value
(cm)
Error
(cm)
Value
(cm/s)
Error
(cm/s)
Value
(cm)
Error
(cm)
Value
(cm)
Error
(cm)
Value
(cm/s)
Error
(cm/s)
520
580
580
580
640
640
640
700
700
700
1
1
1
1
1
1
1
1
1
1
6.0
15.0
10.0
6.0
15.0
10.0
6.0
15.0
10.0
6.0
0.5
0.5
6.9
7.4
7.3
7.0
7.5
7.5
7.0
7.4
7.6
7.0
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
1.1
1.0
1.0
1.1
1.0
1.0
1.1
1.0
1.3
1.0
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.9
0.7
0.8
0.8
0.6
0.7
0.8
0.6
0.7
0.8
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.5
0.4
0.4
0.5
0.4
0.4
0.4
0.4
0.4
0.4
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
770
1
15.0
0.5
7.5
0.1
1.0
0.3
0.6
0.3
0.4
0.3
770
770
1
1
10.0
6.0
0.5
0.5
7.3
7.0
0.1
0.1
1.7
1.0
0.3
0.3
0.8
0.7
0.3
0.3
0.5
0.4
0.3
0.3
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
109
Table 11. Case 4 - Raw velocity data along centerline of flume with standard deviation given.
Flexible Sparse - Case 4
X Position
Z Position
Ux
Urms
Vrms
Wrms
Value
(cm)
Error
(cm)
Value
(cm)
Error
(cm)
Value
(cm/s)
Error
(cm/s)
Value
(cm/s)
Error
(cm/s)
Value
(cm/s)
Error
(cm/s)
Value
(cm/s)
Error
(cm/s)
-95
-95
-95
-50
-50
-50
-50
-50
-50
0
0
0
0
0
10
10
10
22
22
22
30
30
30
50
50
50
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
15.0
10.0
6.0
15.0
15.0
10.0
10.0
6.0
6.0
15.0
15.0
10.0
10.0
6.0
15.0
10.0
6.0
15.0
10.0
6.0
15.0
10.0
6.0
15.0
15.0
10.0
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
7.3
7.2
7.6
7.5
7.2
7.0
8.0
7.1
7.1
7.3
7.4
6.7
7.6
6.2
7.8
5.7
0.3
9.3
7.7
4.7
9.0
7.1
0.1
9.4
10.7
4.6
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
1.5
1.6
1.4
1.4
1.6
1.6
1.3
1.5
1.4
1.3
1.4
1.5
1.5
1.1
1.4
2.9
0.5
1.8
2.3
1.3
1.5
1.8
0.2
1.5
1.8
2.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
1.2
1.3
1.4
1.0
1.2
1.1
1.1
1.2
1.2
1.0
0.9
1.1
1.2
1.0
1.0
1.3
0.4
1.3
1.6
0.9
1.0
1.1
0.2
0.9
1.4
1.6
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.8
0.8
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
110
0.7
0.7
0.7
0.7
0.7
0.6
0.6
0.6
0.6
0.6
0.7
0.5
0.6
0.6
0.1
0.6
0.6
0.4
0.6
0.5
0.1
0.6
0.6
0.8
X Position
Value
(cm)
50
50
50
80
80
80
100
100
100
130
130
130
200
200
200
200
200
200
280
280
280
400
400
400
400
400
400
520
520
Z Position
Error Value
(cm)
(cm)
Error Value
(cm)
(cm/s)
10.0
6.0
6.0
15.0
10.0
6.0
15.0
10.0
6.0
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
15.0
0.5
10.0
6.0
15.0
15.0
10.0
10.0
6.0
6.0
15.0
10.0
6.0
15.0
15.0
10.0
10.0
6.0
6.0
15.0
10.0
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
6.3
-0.2
0.0
7.9
3.5
-0.5
7.8
3.2
1.3
5.6
5.1
2.9
5.8
3.1
5.5
3.7
4.8
5.7
6.2
7.0
5.9
6.7
7.3
7.1
6.7
6.4
6.2
7.1
7.5
Wrms
Vrms
Urms
Ux
Error
(cm/s)
Value
(cm/s)
Error
(cm/s)
Value
(cm/s)
Error
(cm/s)
Value
(cm/s)
Error
(cm/s)
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
2.7
0.5
0.4
2.1
2.8
1.7
2.2
3.4
1.9
2.2
1.8
1.5
1.5
2.2
1.3
3.0
1.4
1.4
1.3
1.3
1.3
1.2
1.2
1.2
1.7
1.1
1.2
1.1
1.1
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
1.8
0.4
0.3
1.5
2.7
1.8
1.5
2.4
2.1
1.8
2.0
1.9
1.3
1.2
1.6
1.4
1.4
1.2
0.9
1.1
1.1
0.8
0.8
1.0
0.9
0.9
0.8
0.7
1.0
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.8
0.2
0.2
0.8
1.0
1.0
0.8
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
111
1.0
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.9
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.9
0.9
0.7
0.8
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.9
0.7
0.8
0.8
0.7
0.6
0.7
0.6
0.5
0.5
0.6
0.6
0.5
0.5
0.4
0.5
X Position
Z Position
Ux
Urms
Vrms
Wrms
Value
Error
Value
Error
Value
Error
Value
Error
Value
Error
Value
Error
(cm)
(cm)
(cm)
(cm)
(cm/s)
(cm/s)
(cm/s)
(cm/s)
(cm/s)
(cm/s)
(cm/s)
(cm/s)
520
580
580
580
640
640
640
700
700
700
770
770
770
1
1
1
1
1
1
1
1
1
1
1
1
1
6.0
15.0
10.0
6.0
15.0
10.0
6.0
15.0
10.0
6.0
15.0
10.0
6.0
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
6.9
7.4
7.3
7.0
7.5
7.5
7.0
7.4
7.6
7.0
7.5
7.3
7.0
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
-
1.1
1.0
1.0
1.1
1.0
1.0
1.1
1.0
1.3
1.0
1.0
1.7
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
-
0.9
0.7
0.8
0.8
0.6
0.7
0.8
0.6
0.7
0.8
0.6
0.8
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
-
0.5
0.4
0.4
0.5
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.5
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
-
-
1.0
-
0.7
-
0.4
-
112
Table 12. Case 4 - Raw deposition data along centerline for each replicate with standard deviation given.
X Position
Value Error
(cm)
(cm)
-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
2
3
6
9
12
15
16
18
19
22
25
26
28
29
31
Flexible Sparse - Case 4
Net Deposition
Net Deposition
Net Deposition
Replicate 3
2
Replicate
1
Replicate
Error
Value
Error
Value
Error
Value
(g/cm 2) (g/cm 2) (g/cm 2) (g/cm 2) (g/cm 2) (g/cm 2)
0.0001
0.0018
0.0001
0.0001
0.0019
0.0023
0.0001
0.0027
0.0001
0.0001
0.0025
0.0008
0.0001
0.0028
0.0026
0.0001
0.0019
0.0001
0.0001
0.0030
0.0001
0.0026
0.0006
0.0001
0.0001
0.0024
0.0026
0.0001
0.0001
0.0009
0.0001
0.0001
0.0031
0.0027
0.0022
0.0001
0.0001
0.0001
0.0029
0.0026
0.0012
0.0001
0.0030
0.0001
0.0026
0.0001
0.0021
0.0001
0.0029
0.0001
0.0001
0.0001
0.0026
0.0022
0.0001
0.0027
0.0001
0.0030
0.0001
0.0025
0.0001
0.0027
0.0001
0.0028
0.0009
0.0001
0.0013
0.0001
0.0001
0.0026
0.0001
0.0023
0.0024
0.0001
0.0001
0.0024
0.0001
0.0013
0.0024
0.0001
0.0001
0.0024
0.0001
0.0014
0.0001
0.0001
0.0023
0.0025
0.0001
0.0013
0.0001
0.0024
0.0001
0.0024
0.0001
0.0015
0.0001
0.0022
0.0001
0.0022
0.0012
0.0001
0.0001
0.0001
0.0024
0.0023
0.0001
0.0012
0.0001
0.0023
0.0001
0.0023
0.0001
0.0010
0.0001
0.0021
0.0001
0.0023
0.0001
0.0018
0.0001
0.0024
0.0001
0.0021
113
Mean Net
Deposition
Error
Value
(g/cm 2)
(g/cmz)
0.0002
0.0020
0.0010
0.0020
0.0024
0.0004
0.0013
0.0020
0.0020
0.0009
0.0026
0.0004
0.0022
0.0009
0.0026
0.0026
0.0027
0.0021
0.0013
0.0024
0.0020
0.0021
0.0020
0.0024
0.0015
0.0022
0.0012
0.0020
0.0023
0.0010
0.0022
0.0018
0.0022
0.0004
0.0004
0.0002
0.0011
0.0002
0.0006
0.0006
0.0006
0.0000
0.0000
0.0007
0.0000
0.0001
0.0002
X Position
Value Error
(cm)
(cm)
33
35
39
42
43
44
45
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
Net Deposition
Replicate 1
Value
Error
(g/cm2) (g/cm2)
0.0021
0.0001
0.0018
0.0001
0.0008
0.0001
0.0017
0.0001
0.0007
0.0018
0.0023
0.0022
0.0023
0.0022
0.0023
0.0022
0.0022
0.0021
0.0023
0.0021
0.0022
0.0022
0.0024
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
210
0.0023
220
230
240
Net Deposition
Replicate 2
Value
Error
(g/cm2) (g/cm2)
0.0024
0.0021
0.0024
0.0001
0.0001
0.0001
Net Deposition
Replicate 3
Value
Error
(g/cm2) (g/cm2)
0.0022
0.0020
0.0001
0.0022
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0026
0.0032
0.0029
0.0027
0.0027
0.0026
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0026
0.0001
0.0026
0.0026
0.0025
0.0025
0.0026
0.0024
0.0025
0.0025
0.0025
0.0025
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0026
0.0033
0.0032
0.0029
0.0028
0.0028
0.0028
0.0027
0.0027
0.0026
0.0025
0.0025
0.0025
0.0024
0.0025
0.0026
0.0026
0.0001
0.0024
0.0001
0.0025
0.0022
0.0001
0.0024
0.0001
0.0021
0.0021
0.0001
0.0001
0.0024
0.0024
0.0001
0.0001
0.0024
0.0001
Mean Net
Deposition
Value
Error
(g/cm2) (g/cm2)
0.0021
0.0022
0.0003
0.0016
0.0007
0.0024
0.0022
0.0017
0.0026
0.0001
0.0024
0.0015
0.0026
0.0008
0.0026
0.0003
0.0026
0.0003
0.0026
0.0003
0.0026
0.0002
0.0025
0.0025
0.0024
0.0024
0.0024
0.0002
0.0002
0.0002
0.0002
0.0003
0.0024
0.0001
0.0023
0.0024
0.0024
0.0025
0.0002
0.0002
0.0002
0.0001
0.0001
0.0024
0.0001
0.0025
0.0001
0.0024
0.0002
0.0026
0.0026
0.0001
0.0001
0.0023
0.0024
0.0003
0.0003
114
X Position
Value Error
(cm)
(cm)
3
250
3
260
3
270
280
3
290
3
3
300
3
310
3
320
3
330
340
3
350
3
3
360
3
370
3
380
3
390
3
400
410
3
420
3
430
3
440
3
450
3
Net Deposition
Replicate 1
Error
Value
(g/cm2) (g/cm2)
0.0001
0.0022
0.0001
0.0021
0.0001
0.0022
0.0020
0.0019
0.0023
0.0022
0.0020
0.0021
0.0022
0.0017
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0021
0.0001
0.0020
0.0017
0.0021
0.0020
0.0019
0.0022
Net Deposition
Replicate 2
Error
Value
(g/cm2) (g/cm2)
0.0001
0.0024
0.0001
0.0026
0.0001
0.0025
0.0001
0.0024
0.0001
0.0024
0.0001
0.0025
0.0001
0.0025
0.0001
0.0025
0.0001
0.0026
Net Deposition
Replicate 3
Error
Value
(g/cm2)
(g/cm2)
0.0001
0.0025
0.0001
0.0026
0.0001
0.0026
0.0001
0.0026
0.0001
0.0025
0.0001
0.0026
0.0001
0.0026
0.0001
0.0026
0.0001
0.0026
0.0001
0.0025
0.0001
0.0026
0.0001
0.0027
0.0001
0.0025
0.0001
0.0026
0.0001
0.0026
0.0026
0.0001
0.0001
0.0026
0.0001
0.0025
Mean Net
Deposition
Error
Value
(g/cm2) (g/cm2)
0.0002
0.0024
0.0003
0.0024
0.0003
0.0025
0.0001
0.0025
0.0003
0.0023
0.0005
0.0023
0.0003
0.0024
0.0003
0.0024
0.0004
0.0024
0.0024
0.0002
0.0024
0.0024
0.0025
0.0024
0.0024
0.0025
0.0025
0.0023
0.0003
0.0004
0.0002
0.0002
0.0003
0.0003
0.0002
0.0005
0.0001
0.0024
0.0003
0.0025
0.0001
0.0026
0.0001
0.0025
0.0001
0.0024
0.0003
0.0003
0.0025
0.0001
0.0025
0.0026
0.0026
0.0026
0.0026
0.0027
0.0026
0.0026
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0026
0.0001
0.0025
0.0026
0.0001
0.0026
0.0001
0.0020
0.0001
0.0025
0.0001
0.0025
0.0001
0.0023
460
3
0.0019
0.0001
470
3
0.0020
0.0001
0.0026
0.0001
0.0025
0.0001
0.0024
0.0003
480
3
0.0014
0.0001
0.0026
0.0001
0.0025
0.0001
0.0022
0.0006
490
500
3
3
0.0022
0.0020
0.0001
0.0001
0.0026
0.0025
0.0001
0.0001
0.0025
0.0024
0.0001
0.0001
0.0024
0.0023
0.0002
0.0003
115
X Position
Value Error
(cm)
(cm)
510
3
520
3
530
3
540
3
550
3
560
3
570
3
580
3
590
3
600
3
610
3
620
3
630
3
640
3
650
3
660
3
670
3
680
3
690
3
700
3
710
3
720
3
730
3
740
3
750
3
760
3
770
3
780
3
Net Deposition
Replicate 1
Value
Error
(g/cm2) (g/cm2)
0.0020
0.0001
0.0021
0.0001
0.0022
0.0001
0.0021
0.0001
0.0018
0.0001
0.0022
0.0001
0.0023
0.0001
0.0021
0.0001
0.0021
0.0001
0.0022
0.0001
0.0021
0.0001
0.0023
0.0001
0.0023
0.0001
0.0025
0.0001
0.0023
0.0001
0.0023
0.0001
0.0024
0.0001
0.0022
0.0001
0.0020
0.0001
0.0019
0.0001
0.0019
0.0001
0.0019
0.0001
0.0014
0.0001
0.0017
0.0001
0.0019
0.0001
0.0022
0.0001
Net Deposition
Replicate 2
Value
Error
(g/cm2) (g/cm2)
0.0026
0.0001
0.0026
0.0001
0.0026
0.0001
0.0025
0.0001
0.0026
0.0001
0.0026
0.0001
0.0025
0.0001
0.0025
0.0001
0.0025
0.0001
0.0025
0.0001
0.0025
0.0001
0.0025
0.0001
0.0025
0.0001
0.0025
0.0001
0.0025
0.0001
0.0025
0.0001
0.0025
0.0001
0.0024
0.0001
0.0025
0.0001
0.0025
0.0001
0.0024
0.0001
0.0024
0.0001
0.0024
0.0001
Net Deposition
Replicate 3
Value
Error
(g/cm2) (g/cm2)
0.0025
0.0001
0.0025
0.0001
0.0025
0.0001
0.0025
0.0001
0.0026
0.0001
0.0025
0.0001
0.0024
0.0001
0.0025
0.0001
0.0025
0.0001
0.0025
0.0001
0.0025
0.0001
0.0025
0.0001
0.0024
0.0001
0.0024
0.0001
0.0025
0.0001
0.0024
0.0001
0.0024
0.0001
0.0025
0.0001
0.0024
0.0001
0.0024
0.0001
0.0024
0.0001
0.0025
0.0001
0.0025
0.0001
0.0024
0.0001
0.0024
0.0001
0.0025
0.0001
0.0024
0.0001
0.0024
0.0001
116
Mean Net
Deposition
Value
Error
(g/cm2) (g/cm2)
0.0024
0.0003
0.0024
0.0003
0.0024
0.0002
0.0024
0.0003
0.0023
0.0004
0.0024
0.0002
0.0024
0.0001
0.0024
0.0002
0.0024
0.0002
0.0024
0.0002
0.0024
0.0002
0.0024
0.0001
0.0024
0.0001
0.0024
0.0001
0.0024
0.0001
0.0024
0.0001
0.0024
0.0000
0.0024
0.0002
0.0023
0.0003
0.0023
0.0004
0.0023
0.0003
0.0023
0.0003
0.0021
0.0006
0.0021
0.0005
0.0021
0.0004
0.0023
0.0002
0.0024
0.0024
X Position
Value Error
(cm)
790
Net Deposition
Replicate 1
Value
Error
Net Deposition
Replicate 2
Value
Error
(cm)
(g/cm2)
(g/cm2)
(g/cm2)
(g/cm2)
3
-
-
-
-
Net Deposition
Replicate 3
Value
Error
(g/cm2) (g/cm2)
0.0025
0.0001
117
Mean Net
Deposition
Value
Error
(g/cm2) (g/cm2)
0.0025
-